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'Qlntver0iti? of Mteconetn 





SoiiDon: C. J. CLAY and SONS, 



Clawgoin: 26S, ABGTLE STKBET. 



ld)i}{0: F. A BBOCKHAUS. 

^cto jgorlt: MACMILLAN AND CO. 





J. A. EWING, M.A., B.Sc., F.R.S., M.In8T.C.E., 

I I 





[AU RighU retened.] 


Cambttlige : 



WHEN I undertook some years ago to prepare an article 
on the Steam-Engine and other Heat- Engines for the 
Encyclopaedia Britannica it seemed that the subject might be 
appropriately treated by following the general lines which had 
been found suitable in lecturing to students of engineering. The 
article was accordingly written on these lines, but necessarily in 
a very condensed form. 

From the time of its publication I have hoped to expand it 
into a University Text-book, and have been encouraged by more 
than one other teacher to believe that such a text-book might be 
useful. The present work is the outcome of that intention : it is 
based on the Encyclopaedia article, but the additions and changes 
have been so considerable that except for parts of one or two 
Chapters the book is virtually new. 

The design has been to treat not only of the thermodjmamics 
of the steam-engine, but of other aspects of the subject which 
admit of theoretical discussion, such as the kinematics of the 
slide-valve and the kinetics of the governor and of the moving 
mechanism as a whole, and also to give a general, if brief, account 
of the forms taken by actual engines and of the manner of their 
working. No attempt has been made to describe details particu- 
larly, but the distinguishing features of certain types have been 
indicated. In doing this the greatest amount of space has been 
given to the less familiar forms, on the principle that a student 
need be at no loss to learn the construction of engines of the 
commoner kinds. Air, gas, and oil engines are noticed, as well 
as steam-engines. 

The endeavour throughout has been to make evident the 
bearing of theory on practical issues. The experimental study 


of Steam-engines, which has done much to bring thermodjmamics 
into closer contact with engineering, is described at some length. 
It is now usual for students to combine their lecture-room study 
of heat-engines with work in the laboratory as well as in the 
drawing office, and parts of the book are designed to serve in 
some measure as a manual for the steam laboratory. 

The Chapters which relate to applied thermodynamics can- 
not of course pretend to give so full a treatment as will be 
found in the valuable books of Professor Cotterill and Professor 
Peabody, which are devoted entirely to that subject. The theory 
of heat-engines is presented here in small compass and in 
elementary form, but I hope it may be found that this section 
is, so far as it goes, complete, and that there are not many 
serious omissions in regard to matters of practical importance. 
I have made considerable use of the entropy-temperature diagram 
as a means of exhibiting thermodjmamic actions, believing that 
this construction only requires to be better known to be widely 
appreciated by engineers. In calculations aflTected by the me- 
chanical equivalent of heat, 778 foot-pounds has been taken as 
the value of Joule's equivalent, the recent work of Griffiths and 
Rowland, in conjunction with the later researches of Joule himself, 
having left no doubt that this number or one closely approxi- 
mating to it is to be accepted in place of the familiar 772. 

I have to thank Messrs A. and C. Black, the publishers of 
the Encyclopdedia Britannica, for consenting to an arrangement 
which allowed some of the material of the article " Steam-Engine " 
to be utilized, and also my present and former assistants, Mr 
W. E. Dalby and Mr T. Reid, for much kind help in preparing 
illustrations. I am indebted for drawings to Messrs Galloway, 
Messrs Gourlay, Messrs Thomycroft, Messrs Willans and Robinson, 
Mr H. Davey, Dr Kirk, Mr C. A. Parsons, Mr F. W. Webb, and 
other engineers. 


Ekoinsering Laboratory, CAiiBRmoE. 
AprU 26, 1894. 





1. Heat-Engines in general 1 

2. Hero of Alexandria ^ 

3. Delia Porta and De Caus 3 

4. Branca's Steam Turbine 4 

5. Marquis of Worcester 4 

6. Savery 5 

7. Gunpowder Engines 7 

8. Papin 7 

9. Newcomen's "Atmospheric" Engine 9 

10. James Watt . 11 

11. Watt's pumping-engine of 1769 13 

12. Watt's narrative of his invention 15 

13. Development of Watt's Engine : the rotative type ... 19 

14. Further improvements by Watt 19 

15. Non-condensing Steam-Engines 21 

16. Use of comparatively high-pressure steam 23 

17. Compound Engines. Homblower and Woolf .... 23 

18. The Cornish Pumping Engine 24 

19. Revival of the Compound Engine 26 

20. Application to locomotives 27 

21. Application to steamboats 28 

22. Development of the Theory of Heat-Engines .... 30 



23. Laws of Thermodynamics. The First Law .... 33 

24. The Second Law of Thermodynamics 36 

25. The Working Substance in a Heat-Engine 35 



26. Graphic Bepresentation of Work done in the changes of yolume 

of a fluid 36 

27. Cycle of operations of the working substance .... 37 

28. Engine using a perfect gas as working substance ... 38 

29. Laws of the permanent gases. Boyle's law .... 39 

30. Charles's law 39 

31. Absolute temperature 40 

32. Connection between Pressure, Volmne, and Temperatxu^ in a gas. 41 

33. The specific heat of a gas 41 

34 The Internal energy of a gas 42 

35. Relation between the two Specific Heats 43 

36. Values of the constants for Air 44 

37. Work done by an expanding fluid 44 

38. Adiabatic Expansion 46 

39. Change of temperature in the adiabatic expan»on of a gas . 47 

40. Isothermal Expansion 48 

41. Camot's Cycle of operations 50 

42. Efficiency in Camot's Cycle 52 

43. Camot's cycle reversed 52 

44. Reversible engine 54 

45. Camot's Principle ; .... 54 

46. Reversibility the criterion of perfection in a heat-engine . . 55 

47. Efficiency of a perfect heat-engine 66 

48. Summary of the argument^ 56 

49. Conditions of maximnm efficiency 57 

50. Conditions of reversibility 58 

51. Perfect Engine using Regenerator 59 

52. Stirhng's Regenerative Air-Engine 60 



53. Formation of steam under constant pressure .... 62 

54. Saturated and superheated steam 63 

55. Relation of pressure and temperature in saturated steam . . 63 

56. Relation of pressure and volume in saturated steam ... 64 

57. Supply of heat in the formation of steam imder constant pressure 66 

58. Latent Heat of Steam 67 

59. Total heat of steam 68 

60. Internal energy of steam 69 

61. Formation of steam otherwise than under constant pressure . 69 

62. Wet steam 70 

63. Superheated steam 70 

64. Isothermal Lines for Steam . . . . . . . • 71 




66. Adiabatic Lines for Steam 72 

66. Formula connecting pressure with volume in the adiabatic expan- 

sion of steam 74 

67. Camot's cycle with steam for working substance ... 75 

68. Efficiency of a perfect steam-engine. Limits of temperature . 77 

69. Efficiency of an engine using steam non-expansively . . 78 

70. Engine with separate organs 79 

71. How nearly may the process in a steam-engine be reversible? 81 











Rankine's statement of the Second Law 86 

Absolute Temperature : Lord Kelvin's scale .... 86 
Calculation of the Density of Saturated Steam ... 87 
Extension of the above result to other changes of physical state . 90 
Drying of steam by throttling or wire-drawing . . . . 91 
Engine receiving heat at various temperatures .... 92 
Application to the case of a steam-engine working without com 

pression, but with complete adiabatic expansion . 
Extension to the case of steam not initially dry 
Derivation of the adiabatic equation from this result 


Entropy of Steam : Derivation of the Adiabatic Equation 

Entropy-Temperature Diagrams 

Entropy-Temperature Diagram for Steam : application to ideal 

steam-engine working without compression but with complete 


Application of the entropy-temperature diagram to the case of 

superheated steam 106 

Values of the Entropy of Water and Steam .... 107 
Entropy-temperature diagram for Steam used non-expansively 111 

Incomplete expansion 112 

Entropy-temperature diagrams in engines using a Regenerator 114 

Joule's Air-Engine 116 

Reversal of the cycle in heat-engines : Refrigerating Machines or 

Heat-Pumps 118 

Coefficient of Performance of Refrigerating Machines . . 121 
Reversed Jorde Engine : the Bell-Coleman refrigerating machine 122 
The Reversed Heat-Engine as a Warming Machine . .124 

Heat-Engines employing more than one working substance : 

Steam and Ether Engines 126 

Transmission of Power by Compressed Air .... 127 












97. Comparison of actual and ideal indicator diagrams . . .131 

98. Wire-drawing during Admission and Exhaust .... 132 

99. Clearance 134 

100. Compression 134 

101. Cushion Steam and Cylinder Feed 136 

102. Influence of the Cylinder Walls. Condensation and Be-evapora- 

tion in the Cylinder 136 

103. Re-evaporation continued during the exhaust .... 138 
104 Wetness of the working steam 139 

105. Graphic Representation, on the Indicator Diagram, of the water 

present during expansion 140 

106. Use of the Entropy-Temperature diagram in exhibiting the 

behaviour of steam during expansion and the exchanges of 

heat between it and the cylinder walls 142 

107. Thermodynamic Loss due to Initial Condensation . . . 144 

108. Action of a Steam-jacket 144 

109. Influence of Speed, Size, and Ratio of Expansion . . . 146 

110. Results of Experiments with various ratios of Expansion . 148 

111. Advantage of high speed 150 

112. Experiments on the value of the Steam-jacket . . . .151 

113. Superheating 152 

114. Advantage of Compound Expansion 154 

115. Summary of Sources of Loss 155 

116. Methods of stating the performance of Steam-Engines . . 156 

117. Efficiency of boiler and furnace. "Duty" . . . .157 

118. Results of Trials : Non-Condensing Engines .... 159 

119. Results of Trials : Condensing Engines . . . . .161 

120. Mechanical Efficiency of the Engine 167 

121. Curve of Expansion to be assumed in estimating the probable 

indicated horse-power of steam-engines 168 



122. The Indicator 169 

123. Conditions of accurate working 172 

124. Directions for taking Indicator Diagrams 175 

125. Calculation of the Indicated Horse- Power 176 

126. Examples of Indicator Diagrams 177 

127. Thermodynamic Tests. Measurement of the Supply of Steam by 

means of the Feed 179 



128. Measurement of the Supply of Steam by means of the Ck)nden8ed 

Water 181 

129. Measurement of Jacket steam 182 

130. Comparison of Feed-water with Discharged Water . . . 182 

131. Estimation of Heat supplied. Measurement of Dryness of the 

Steam by the "BarreP Calorimeter 183 

132. Barrus Calorimeter 184 

133. Peabody Throttling Calorimeter 184 

134 Measurement of Heat rejected by an Engine .... 185 

136. Example of an Engine Trial 187 

136. Wetness of the steam during expansion 189 

137. Transfer of Heat between the Steam and the MetaL Him's 

Analysis 190 

138. Tests of mechanical efficiency. Measurement of Brake Horse- 

power 192 

139. Trials of an engine under various amounts of load . . . 193 



140. Woolf Engines 197 

141. Eeceiver engine 198 

142. Drop in the Receiver. Compound diagrams .... 198 

143. Adjustment of the division of work between the cylinders, and 

of the drop. Qraphic method 201 

144. Algebraic Method 203 

145. Ratio of Cylinder Volmnes 204 

146. Advantage of Compound Expansion in the economical use of 

High-Pressure Steam 206 

147. Mechanical advantage of Compound Expansion. Uniformity of 

E£fort in a Compound Engine 206 

148. Examples of Indicator Diagrams from Compound Engines . 208 

149. Combination of the Indicator Diagrams in Compound Ex- 

pansion 209 



160. The Slide-Valve 215 

151. Lap, Lead, and Angular Advance 216 

152. Graphic method of examining the distribution of steam given 

by a slide-valve 219 


ABT. 'AO« 

153. Inequalitj of the distribution on the two sides of the piston . 222 

164. Zeuner^B Valve Diagram 225 

156. Oval Diagram 228 

156. Harmonic Diagram 229 

157. Reversing Qear. The link-motion 232 

168. Graphic Solution of the Link-motion 235 

169. Equivalent eccentric 236 

160. Radial Gears 237 

161. Separate expansion-valves 240 

162. Meyer's Expansion-valve 241 

163. Forms of slide-valves. Double-ported valve. Trick valve . 246 

164. Relief Frames 247 

165. Piston Valves 249 

166. Rocking slide-valve 249 

167. Double-beat valve. The Cornish cataract 260 



168. Methods of r^ulating the work done in a Steam-engine . . 252 

169. Automatic r^ulation by centrifugal speed governors. Watt's 

Conical Pendulum Governor 263 

170. Loaded Governors 253 

171. Controlling Force 255 

172. Condition of Equilibrium 255 

173. Condition of Stability 256 

174. Equilibrium of the Conical Pendulum Governor. Height of the 

Governor 256 

175. Equilibrium of Loaded Governor 257 

176. Sensibility in a Governor. Isochronism 259 

177. Isochronism in the Gravity Governor. Parabolic Governor . 260 

178. Approximate Isochronism in Pendulum Governors . . 261 

179. Governors with spring control. Adjustment of sensitiveness . 263 

180. Determination of the Controlling Force 263 

181. Influence of Friction. Power of the Governor .... 264 

182. Curves of Controlling Force 266 

183. Hunting 268 

184. Governor with horizontal axis 269 

185. Throttle-valve and automatic expansion-gear .... 270 

186. Corliss and other Trip-gear 270 

187. Disengagement governors 274 

188. Relay governors 276 

189. Differential or dynamometric governors 276 

190. Pump governors 278 

191. Governing marine engines 279 





192. Fluctuations of Speed during any single revolution : function 

of the Fly-wheel 280 

193. Diagram of crank-effort 280 

194. Effect of Friction 282 

195. Effect of the inertia of the reciprocating pieces . . . 283 

196. Inertia of the Connecting-rod 285 

197. Treatment of Inertia and Friction together .... 287 

198. Forms of Crank-Effort Diagrams 289 

199. Fluctuation of Speed in relation to the Enei^gy of the Fly- 

wheel 290 

200. Keversal of thrust at the joints. Prevention of reversal of the 

thrust in single-acting engines 292 

201. Balancing . 294 



202. Heating Surface, in Boiler and Feed-water Heater . . . 298 

203. Draught 299 

204. Sources of loss of Heat 301 

205. Chimney Draught 302 

206. Boilers for Stationary Engmes. Cornish and Lancashire Types 303 

207. Boiler Mountings 307 

208. Multitubular Boilers 307 

209. Vertical Boilers 308 

210. Watertube Boilers 309 

211. Locomotive Boilers 312 

212. Marine Boilers . . . 316 

213. Feeding boilers. The Injector 318 

214. Feed-water heaters 320 

215. Use of Zinc to prevent corrosion in boilers .... 320 

216. Methods of forcing draught . . . . . . .321 

217. Mechanical Stoking 322 

218. Liquid Fuel 322 





219. Terms used in classification 324 

220. Beam-Engines 325 

221. Direct-acting Horizontal and Vertical Engines .... 326 

222. Single-acting high speed Engines 329 

223. Pimiping Engines 334 

224 The pulsometer 338 

225. Davey's safety motor 339 

226. Rotary Engines 340 

227. Steam Turbines . 342 

228. Marine Engines 346 

229. Relation of power to weight in Marine Engines . . . 349 

230. Locomotives 350 

231. Compound Locomotives 352 

232. Tramway and Road Locomotives 354 



233. Air and Gas-engines with external or internal combustion . 357 

234 Air-engine using Camot's cycle 358 

235. External Combustion Air-engine with Regenerator: Stirling, 

Ericsson 358 

236. Modem Air-engines of the Stirling type 361 

237. Internal Combustion Air-engines 365 

238. Early Qas-engines 367 

239. The four-stroke cycle of Beau de Rochas and Otto ... 368 

240. The Otto Engine 369 

241. Other Gas-engines 371 

242. Action in the cylinder of the Otto Engine .... 373 

243. After-burning 374 

244 Performance of Gas-engines 377 

245. Ideal performance of an internal combustion engine . . 380 

246. Use of cheap gas 381 

247. Oil-engines 383 


INDEX 391 



1. Heat-Engines in general In the scientific treatment 
of the steam-engine we have in the first place, and mainly, to 
regard it as a heat-engine — ^that is, a machine in which heat 
is employed to do mechanical work. Other aspects of the steam- 
engine will present themselves when we come to examine the 
action of the mechanism in detail, but the foremost place must be 
given to thermodynamic considerations. From the thermo- 
djmamic point of view the function of a heat-engine is to get 
as much work as possible from a given supply of heat, or (to go 
a step further back) from the combustion of a given quantity 
of fuel. Hence a large part of our subject is the discussion of 
what is called the efficiency of the engine, which is the ratio 
of the work done to the heat supplied. We hiave to consider on 
what conditions efficiency depends, how its value is limited in 
theory and how nearly the limiting value may be attained in 
practice. We have to describe means of testing the efficiency of 
engines, and the results which such tests have given in actual 
oases. Much of what has to be said in regard to efficiency is 
applicable to all heat-engines, whatever be the character of the 
substance the expansion of which is made use of as the means of 
doing work within the engine. In all practical heat-engines work 
is done through the expansion by heat of a fluid which exerts 
pressure and overcomes resistance as it expands. Thus in steam- 
engines the working substance is water and water-vapour, and 
work is done by the pressure which the substance exerts while its 
volume is undergoing change. In air-engines the working substance 
E. 1 


is atmospheric air ; in gas-engines and oil-engines it is a mixture 
of air with combustible gas or vaporised oil and with the products 
of combustion. These last are important instances of what are 
sometimes called internal combustion engines, in which the 
heat is developed by combustion occurring within the working- 
substance itself instead of reaching the substance from an 
external source. We may have heat-engines in which the working 
substance is not a fluid, and examples might even be named 
in which a substance that is alternately heated and cooled is 
made to do work not in consequence of changes in its volume or 
in its form, but in consequence of some other effect of heat such, for 
instance, as the loss and gain of magnetic quality. A complete list 
of typical heat-engines would include a mention of guns, in which 
the heat that is generated by the combustion of an explosive 
does work in giving energy of motion to a projectile. We have, 
however, to do only with those types of heat-engine whose object 
is to change the potential energy of fuel into a manageable 
mechanical form, so that they may serve as prime movers to other 
mechanism. Of such engines the steam-engine is by &r the most 

As a preliminary to the study of the modem engine it will 
be useful to review, if only very briefly, some of the stages 
through which it has passed in its development. In any such 
historical sketch by far the largest share of attention necessarily 
falls to the work of Watt, whose inventions were as remarkable 
for their scientific interest as for their industrial importance. 
But it should be borne in mind that a process of evolution had 
been going on before the time of Watt which prepared the 
steam-engine for the immense improvements it received at his 
hands. The labours of Watt stand in natural sequence to those 
of Newcomen, and Newcomen's to those of Papin and Saveiy. 
Savery's engine, again, was the reduction to practical form of a 
contrivance which had long before been known as a scientific toy. 

2. Hero of Alexandria. The earliest notices of heat- 
engines are found in the Pneumatics of Hero of Alexandria, 
which dates from the second century before Christ. One of the 
contrivances mentioned there is the aeolipile, a steam reaction- 
turbine consisting of a spherical vessel pivoted on a central axis 
and supplied with steam through one of the pivots. The steam 


escapes by bent pipes £Etcing tangentially in opposite directions, 
at opposite ends of a diameter perpendicular to the axis. The 
globe revolves by reaction firom the escaping steam, just as a 
Barker's mill is driven by escaping water. Another apparatus 
described by Hero (fig. 1)* is interesting as the prototype of 
a class of engines which long afterwards became practically 
important. A hollow altar containing air is heated by a fire 
kindled on it; the air in expanding drives some of the water 
contained in a spherical vessel beneath the altar into a bucket, 
which descends and opens the temple doors above by pulling 
round a pair of vertical posts to which the doors are fixed. When 
the fire is extinguished the air cools, the water leaves the 
bucket, and the doors close. In another device a jet of water 
driven out by expanding air is turned to account as a fountain. 
Several other philosophical toys or pieces of conjuring apparatus 
of the like kind are abo described but there is no suggestion 
that the methods they illustrate could be applied on a large 
scale or turned to any useful account. 

Fig. 1. Apparatus described by Hero. 

3. Delia Porta and De Caus. From the time of Hero 
to the 17 th century there is no progress to record, though here 

1 From Qreenwood's translation of Hero's Pneumatia, edited hy B. Woodcroft, 



and there we find evidence that appliances like those described 
by Hero were used for trivial purposes, such as organ-blowing 
and the turning of spita The next distinct step was the 
publication in 1606 of a treatise on pneumatics by Giovanni 
Battista della Porta, in which he shows an apparatus similar to 
Hero's fountain, but with steam instead of air as the displacing 
fluid. Steam generated in a separate vessel passed into a closed 
chamber containing water, and drove the water out through a 
pipe which opened near the bottom of the vessel. He also points 
out that the condensation of steam in the closed chamber may 
be used to produce a vacuum and suck up water from a lower 
level. In fact, his suggestions anticipate very fiilly the principle 
which a century later was applied by Savery in the earliest com- 
mercially successful steam-engine. In 1615 Salomon de Cans 
gives a plan of forcing up water by a steam-fountain which 
diflCers from Porta's only in having one vessel serve both as 
boiler and as displacement-chamber, the hot water being itself 

4. Branca'8 Steam Turbine. Another line of invention 
was taken by Giovanni Branca (1629), who designed an engine 
shaped like a water-wheel, to be driven by the impact of a jet of 
steam on its vanes, and, in its turn, to drive other mechanism for 
various useful purposes. But Branca's suggestion was unpro- 
ductive, and we find the course of invention revert to the line 
followed by Porta and De Causr 

6. Marquis of Worcester. The next contributor is one 
whose place is not easily assigned. To Edward Somerset, second 
marquis of Worcester, appears to be due the credit of proposing, if 
not of making, the first useful steam-engine. Its object was to 
raise water, and it worked probably like Portals model, but with a 
pair of displacement-chambers, from each of which alternately 
water was forced by steam from an independent boiler, or perhaps 
by applying heat to the chamber itself, while the other vessel was 
allowed to refill. The only description of the engine is found in 
Art. 68 of Worcester's Century of Inventions (1663). There are 
no drawings, and the notice is so obscure that it is difiicult to say 
whether there were any distinctly novel features except the 
double action. The inventor's account leaves much to the imagi- 
nation. It is entitled " A Fire Water- work," and runs thus : — 


" An admirable and most forcible way to drive up water by fire, not by drawing 
or Buddng it upwards, for that must be as the Philosopher calleth it, Intra 
tphaeram activitatis, which is but at such a distance. But this way hath no 
Bounder, if the Vessels be strong enough ; for I have taken a piece of a whole 
Cannon, whereof the end was burst, and filled it three-quarters full of water, 
stopping and scruing up the broken end ; as also the Touch-hole ; and making a 
constant fire under it, within 24 hours it burst and made a great crack. So that 
having a way to make my Vessels, so that they are strengthened by the force within 
them, and the one to fill after the other, I have seen the water run like a constant 
Fountaine-stream forty foot high; one Vessel of water rarified by fire driveth 
up forty of cold water. And a man that tends the work is but to turn two 
Cocks, that one Vessel of water being consumed, another begins to force and 
re-fill with cold water, and so successively, the fire being tended and kept constant, 
which the self-same Person may likewise abundantly perform in the interim 
between the necessity of turning the said Cocks." 

Later articles in the Century of Inventions contain notices of a 
device which under the name of a " Water-commanding Engine " 
received protection by Act of Parliament and was experimented on 
by Worcester on a large scale at Vauxhall. But there is nothing 
to show distinctly that the Water-commanding Engine was a heat- 
engine at ail, and the meagre accounts that have been given of it 
rather point to the conclusion that it was a form of " Perpetual 
Motion." In any case the experiments led to no practical result. 

6. Saveiy. The steam-engine became commercially success- 
ful in the hands of Thomas Savery, who in 1698 obtained a 
patent for a water-raising engine, shown in fig. 2. Steam is 
admitted to one of the oval vessels A, displacing water, which 
it drives up through the check-valve B. When the vessel A 
is emptied of water, the supply of steam is stopped, and the 
steam already there is condensed by allowing a jet of cold water 
from a cistern above to stream over the outer surface of the vessel. 
This produces a vacuum and causes water to be sucked up through 
the pipe C and the valve D. Meanwhile, steam has been displacing 
water from the other vessel, and is ready to be condensed there. 
The valves B and D open only upwards. The supplementary 
boiler and furnace £ are for feeding water to the main boiler ; E is 
filled while cold and a fire is lighted under it ; it then acts like the 
vessel of De Caus in forcing a supply of feed- water into the main 
boiler F. The gauge-cocks G, G for testing the level of the water 
in the boiler are an interesting feature of detail. Another form of 
Savery's engine had only one displacement-chamber and worked 
intermittently. In the use of artificial means to condense the steam. 



and in the application of the vacuum so formed to raise water 
by suction from a level lower than that of the engine, Savory's 
engine was probably an improvement on Worcester's ; in any case 
it was the first engine to take a really practical shape. It found 

Fio. 2. — Savery's Pumping Engine, 1698. 

considerable employment in pumping mines and in raising water 
to supply houses and towns, and even to drive water-wheels. 
A serious difficulty which prevented its general use in mines 
was the fact that the height through which it would lift water 
was limited by the pressure the boiler and vessels could bear. 
Pressures as high as 8 or 10 atmospheres were employed-^and 
that, too, without a safety-valve. But Savery found it no easy 
matter to deal with high-pressure steam; he complains that it 
melted his common solder, and forced him, as Desaguliers tells 
us, " to be at the pains and charge to have all his joints soldered 
with spelter." Apart from this drawback the waste' of fuel was 
enormous, from the condensation of steam which took place on 
the surface of the water and on the sides of the displacement- 
chamber at each stroke; the consumption of coal was, in pro- 
portion to the work done, some twenty times greater than in a 


good modern steam-engine. In a tract called The Miner's Friend^ 
Savery alludes thus to the alternate heating and cooling of the 
water- vessel : " On the outside of the vessel you may see how the 
water goes out as well as if the vessel were transparent, for so Bar 
as the steam continues within the vessel so fiar is the vessel dry 
without, and so very hot as scarce to endure the least touch of 
the hand. But as far as the water is, the said vessel will be cold 
and wet where any water has fisiUen on it; which cold and 
moisture vanishes as fast as the steam in its descent takes place 
of the water." Before Savory's engine was entirely displaced by 
its successor, Newcomen's, it was improved by Desaguliers, who 
applied to it the safety-valve (invented by Papin), and substituted 
condensation by a jet of cold water within the vessel for the 
surface condensation used by Savery. 

To Savery is ascribed the first use of the familiar term " horse- 
power" as a measure of the performance of an engine. 

7. Qunpowder Engines. Some twenty years before the 
date of Savery's patent, proposals had been made by several 
inventors to raise water by means of the explosive power of 
gunpowder. One scheme was to explode the powder in a closed 
vessel furnished with valves which opened outwards and allowed 
a great part of the air and burnt gases to escape when the 
explosion took place. As the gas that remained became cool 
a partial vacuum was formed in the vessel, and this was used to 
draw up water from a lower level. It does not appear that these 
schemes were ever put in practice except experimentally. The 
most interesting of the gunpowder engines was that of Huygens 
{1680), who for the first time introduced the piston and cylinder 
as constituent parts of a heat-engine. In Huygens' engine the 
piston was set at the top of a vertical cylinder and a charge of 
powder was exploded below it. This expelled part of the gaseous 
contents through valves which opened outwards, and then the 
cooling of the remainder caused the piston to descend under 
atmospheric pressure. The piston in descending did work by 
raising a weight through the medium of a cord and pulley. 

8. Papin. In 1690 Denis Papin, who ten j^ears before had 
invented the safety-valve as an adjunct to his " digester," suggested 
that the condensation of steam should be employed to make a 
vacuum under a piston which had been previously raised by the 



expansion of the steam. Papin had been associated with Huygens 
in his experiments on the production of a vacuum under a piston 
by means of gunpowder, and had described Huygens' machine to 
the Boyai Society. Noticing that after the explosion enough gas 
remained in the cylinder to fill about one-fifth of its volume, after 
cooling, he cast about for some means of obtaining a better 
vacuum. "By another way, therefore, I endeavoured to attain 
the same end, and since it is a property of water that a small 
quantity of it, converted into steam by heat, has an elastic force 
like that of air, but when cold supervenes, is again resolved into 
water so that no trace of the said elastic force remains, I saw 
that machines might be constructed wherein water, by means 
of no very intense heat and at small cost, might produce that 
perfect vacuum which had foiled to be obtained by the use of 
gunpowder." He goes on to describe what was unquestionably 
the earliest cylinder and piston steam-engine, and his plan of 

Fio. 8. — Papin's modification of Savery's Engine, 1705. 

using steam was that which afterwards took practical shape in 
the atmospheric engine of Newcomen. But his scheme was 
made unworkable by the fact that he proposed to use but one 
vessel as both boiler and cylinder. A small quantity of water 
was placed at the bottom of a cylinder and heat was applied. 
When the piston had risen the fire was removed, the steam was 
allowed to cool, and the piston did work in its down-stroke under 
the pressure of the atmosphere. 

After hearing of Savory's engine in 1705 Papin turned his 
attention to improving it, and devised a modified form, shown 


in fig. 3, in which the displacement-chamber A was a cylinder, 
with a floating diaphragm or piston on the top of the water to 
keep the water and steam from direct contact with one another. 
The water was delivered into a closed air-vessel B, from which 
it issued in a continuous stream against the vanes of a water- 
wheel. After the steam had done its work in the displacement- 
chamber it was allowed to escape by the stop-cock C instead of 
being condensed. This second engine of Papin's was in fact a 
non-condensing single-acting steam-pump, with steam-cylinder 
and pump-cylinder in one. A curious feature of it was the heater 
D, a mass of hot metal placed in the diaphragm for the purpose 
of keeping the steam dry. Among the many inventions of Papin 
was a boiler with an internal fire-box, — the earliest example of a 
construction that is now almost universal^. 

9. Newcomen'8 '' Atmospheric '' Engine. While Papin 

was thus going back from his first notion of a piston-engine to 

Savery's cruder type, a new inventor had appeared who made the 

piston-engine a practical success by separating the boiler from the 

cylinder and by using (as Savery had done) artificial means to 

condense the steam. This was Newcomen, who in 1705, in 

conjunction with Savery and with Cawley, gave the steam-engine 

the form shown in fig. 4. Steam admitted from the boiler to the 

cylinder allowed the piston to be raised by a heavy counterpoise 

on the other side of the beam. Then the steam-valve was shut 

and a jet of cold water entered the cylinder and condensed the 

steam. The piston was consequently forced down by the pressure 

of the atmosphere and did work on the pump through the medium 

of a long rod which hung from the other end of the beam. The 

next entry of steam expelled the condensed water from the 

cylinder through an escape valve. The piston was kept tight by 

a layer of water on its upper surface. Condensation was at first 

eflFected by cooling the outside of the cylinder, but an accidental 

leakage of the packing water past the piston showed the advantage 

of condensing by a jet of injection water, and this plan took the 

place of surface condensation. The engine used steam which 

had a pressure little if at all greater than that of the atmosphere ; 

sometimes indeed it was worked with the manhole-lid off the 

^ For an account of Papin's inventions, see his Life, and Corretpondence with 
Leibnitz and Huygens, by Dr £. Qerland, Berlin, 1881. See also Moirhead's Life 
of Watt. 



boiler. The function of the steam was merely to allow the piston 
to be raised, by making the pressure on the under side equal 

Fio. 4. — ^Newoomen's Atmospheric Engine, 170o. 

or nearly equal to the pressure on the top, and then to produce 
a vacuum by being condensed. Newcomen's engine was essentially 
the cylinder and piston of Papin combined with the separate boiler 
of Savery. 

About 1711 Newcomen's engine began to be introduced for 
pumping mines. It is doubtful whether the engine was originally 
automatic in its action or depended on the periodical turning of 
taps by an attendant. An old print of an engine erected by 
Newcomen in 1712 near Dudley Castle shows a species of auto- 
matic gear. The common story is that in 1713 a boy named 
Humphrey Potter, whose duty it was to open and shut the valves 
of an engine he attended, made the engine self-acting by causing 
the beam itself to open and close the valves by means of cords 


and catches. This rude device was simplified in 1718 by Henry 
Beighton, who suspended from the beam a rod called the plug- 
tree, which worked the valves by means of tappets. By 1725 the 
engine was in common use in collieries, and it held its place 
without material change for about three-quarters of a century in 
all. Near the close of its career the atmospheric engine was 
much improved in its mechanical details by Smeaton, who built 
many large engines of this type about the year 1770, just after 
the great step which was to make Newcomen's engine obsolete 
had been taken by James Watt. 

Like Savory's engine, Newcomen's was put to no other use 
than to pump water — in some instances for the purpose of turning 
water-wheels to drive other machinery. Compared with Savory's 
it had the great advantage that the intensity of pressure 
in the pump was not in any way limited by the pressure of 
the steam, but could be made as great as might be desired by 
reducing the area of the pump plunger. It shared with Savory's, 
in a scarcely less degree, the defect already pointed out, that 
steam was wasted by the alternate heating and cooling of the 
vessel into which it was led. Even contemporary writers complain 
of its "vast consumption of fuel," which appears to have been 
scarcely smaller than that of the engine of Savory. 

10. James Watt In 1763 James Watt, an instrument 
maker in Glasgow, while engaged by the University in repairing a 
model of Newcomen's engine, was struck with the waste of steam 
to which the alternate chilling and heating of the cylinder gave 
rise. He saw that the remedy, in his own words, would lie in 
keeping the cylinder as hot as the steam that entered it. With 
this view he added to the engine a new organ — namely, the con- 
denser — a vessel separate from the cylinder, into which the steam 
should be allowed to escape from the cylinder, to be condensed 
there by the application of cold water either outside or as a jet. 
To preserve the vacuum in his condenser he added a pump, 
called the air-pump, whose function was to pump from it the 
condensed steam and water of condensation, as well as the air 
which would otherwise accumulate by leakage inwards or by being 
brought in with the steam or with the injection water. Then as 
the cylinder was itself no longer used as the chamber in which the 
steam was condensed he was able to keep it continuously hot by 



clothing it with non-conducting bodies, and in particular by the 
use of a Steam-jacket, or layer of hot steam between the cylinder 
and an external casing. Further, and still with the same object, 
he covered in the top of the cylinder, taking the piston-rod out 
through a steam-tight stuffing-box, and allowed steam instead of 
air to press upon the piston's upper sur&ce. The idea of using 
a separate condenser had no sooner occurred to Watt than he put 
it to the test by constructing the 
apparatus shown in fig. 5. There A 
is the cylinder, B a condenser (of 
the type now distinguished as a sur- 
face-condenser) and C is the air-pump. 
The cylinder was filled with steam 
above the piston, and a vacuum was 
formed in the surface-condenser B. 
On opening the stop-cock D the 
steam rushed over from the cylinder 
and was, condensed, while the piston 
rose and lifted a weight. A fuller 
account of this experiment will be 
found in Watt's narrative, below. 

After several trials Watt patented his improvements in 1769; 
they are described in his specification in the following words, 
which, apart from their immense historical interest, deserve 
careful study as a statement of principles which to this day 
guide the scientific development of the steam-engine : — 

** My method of lessening the consumption of steam, and consequently fuel, in 
fire-engines, consists of the following principles : — 

* ' Fint^ That vessel in which the powers of steam are to be employed to work 
the engine, which is called the cylinder in conmion fire-engines, and which I call 
the steam-vessel, must, during the whole time the engine is at work, be kept as hot 
as the steam that enters it ; first by enclosing it in a case of wood, or any other 
materials that transmit heat slowly; secondly, by surrounding it with steam or 
other heated bodies ; and, thirdly, by sufFering neither water nor any other substance 
colder than the steam to enter or touch it during that time. 

'* Secondly, In engines that are to be worked wholly or partially by condensation 
of steam, the steam is to be condensed in vessels distinct from the steam-vessels or 
cylinders, although occasionally communicating with them; these vessels I call 
condensers ; and, whilst the engines are working, these condensers ought at least to 
be kept as cold as the air in the neighbourhood of the engines, by application of 
water or other cold bodies. 

** Thirdly, Whatever air or other elastic vapour is not condensed by the cold of 
the condenser, and may impede the working of the engine, is to be drawn out of the 

Fio. 6. 
Watt's Experimental Apparatus. 


steam-vessels or condensers by means of pomps, wrought by the engines themselves, 
or otherwise. 

*' Fourthly J I intend in many cases to employ the expansive force of steam to 
press on the pistons, or whatever may be used instead of them, in the same manner 
as the pressure of the atmosphere is now employed in common fire-engines. In 
cases where cold water cannot be had in plenty, the engines may be wrought by 
this force of steam only, by discharging the steam into the open air after it has done 
its ofiQce 

'* Sixthly, I intend in some cases to apply a degree of cold not capable of 
reducing the steam to water, but of contracting it considerably, so that the engines 
shall be worked by the alternate expansion and contraction of the steam. 

** Lastly, Instead of using water to render the pistons and other parts of the 
engine air and steam-tight, I employ oils, wax, resinous bodies, fat of animals, 
quicksilver and other metals in their fluid state." 

The fifth claim was for a rotary engine, and need not be 
quoted here. 

The ** common fire-engine " alluded to was the steam-engine, 
or, as it was more generally called, the " atmospheric " engine of 
Newcomen. Enormously important as Watt's first patent was, it 
resulted for a time in the production of nothing more than a 
greatly improved engine of the Newcomen type, much less 
wasteful of fuel, able to make faster strokes, but still only suitable 
for pumping, still single-acting, with steam admitted during the 
whole stroke, the piston still pulling the beam by a chain 
working on a circular arc. The condenser was generally kept cool 
by the injection of cold water, but Watt has left a model of a 
surface-condenser made up of small tubes, in every essential 
respect like the condensers now used in marine engines. He also 
used, as we have seen, a surface-condenser in the experimental 
apparatus by which the practicability of condensation in a 
separate vessel was first demonstrated. 

11. Watt'8 pumping-engine of 1769. Fig. 6 is an 
example of the Watt pumping-engine of this period. It should 
be noticed that, although the top of the cylinder is closed and 
steam has access to the upper side of the piston, this is done only 
to keep the cylinder and piston warm. The engine is still single- 
acting ; the steam on the upper side merely plays the part which 
was played in Newcomen's engine by the atmosphere; and it is 
the lower end of the cylinder alone that is ever put in com- 
munication with the condenser. There are three valves, — the 
" steam " valve a, the " equilibrium " valve b, and the " exhaust '' 



valve c. At the beginning of the down-stroke c is opened to 
produce a vacuum below the piston and a is opened to admit 
steam above it. At the end of the down-stroke a and c are shut 

1 — I — r 

Fig. 6. Watt's Single-actmg Engine, 1769. 

and b is opened. This puts the two sides of the piston in 
equilibrium, and allows the piston to be pulled up by the pump- 
rod P, which is heavy enough to serve as a counterpoise. C is the 
condenser, and A the air-pump, which discharges into the hot well 
H, whence the supply of the feed-pump F is drawn. 


12. Watt's narratiTe of hii inyentioii. In a note ap- 
pended to the article " Steam-Engine " in Robison's "System of 
Mechanical Philosophy" (1822) Watt has given the following 
account of the experiments and reflexions which led up to his first 
patent. This narrative is of so particular interest that no apology 
need be made for reproducing it in full. 

** My attention was first directed in the year 1759 to the subject of steam-engines, 
bj the late Dr Bobison himself, then a stndent in the University of Glasgow, and 
nearly of my own age. He at that time threw out an idea of applying the power of 
the steam-engine to the moving of wheel-carriages, and to other purposes, but the 
scheme was not matured, and was soon abandoned on his going abroad. 

About the year 1761 or 1762, 1 tried some experiments on the force of steam, in 
a Papin's digester, and formed a species of steam-engine by fixing upon it a syringe 
one-third of an inch diameter, with a solid piston, and furnished also with a cock 
to admit the steam from the digester, or shut it off at pleasure, as well as to open a 
communication from the inside of the syringe to the open air, by which the steam 
contained in the syringe might escape. When the communication between the 
digester and syringe was opened, the steam entered the syringe, and by its 
action upon the piston raised a considerable weight (15 lbs.) with which it waa 

VfThen this was raised as high as was thought proper, the communication with 
the digester was shut, and that with the atmosphere opehed ; the steam then made ita 
escape, and the weight descended. The operations were repeated, and though in this 
experiment the cock was turned by hand, it was easy to see how it could be done by 
the machine itself, and to make it work with perfect regularity. But I soon 
relinquished the idea of constructing an engine upon this principle, from being 
sensible it would be liable to some of the objections against Savery's engine, viz. the 
danger of bursting the boiler, and the difficulty of making the joints tight, and also 
that a great part of the power of the steam would be lost, because no vacuum was 
formed to assist the descent of the piston. [I, however, described this engine in the 
fourth article of the specification of my patent of 1769 ; and again in the specifica- 
tion of another patent in the year 1784, together with a mode of applying it to the 
moving of wheel-carriages.] 

The attention necessary to the avocations of business prevented me from then pro- 
secuting the subject farther ; but in the winter of 1763-4, having occasion to repair a 
model of Newcomen's engine belonging to the Natural Philosophy dass of the 
University of Glasgow, my mind was again directed to it. At that period, my know- 
ledge was derived principally from Desaguliers, and partly from Belidor. I set about 
repairing it as a mere mechanician, and when that was done and it was set to work, 
I was surprised to find that its boiler could not supply it with steam, though appa- 
rently quite large enough (the cylinder of the model being two inches in diameter 
and six inches stroke, and the boiler about nine inches diameter). By blowing the 
fire it was made to take a few strokes, but required an enormous quantity of in- 
jection water, though it was very lightly loaded by the column of water in the 
pump. It soon occurred that this was caused by the little cylinder exposing a 
greater surface to condense the steam than the cylinders of larger engines did 
in proportion to their respective contents. It was found that by shortening the 
OQlmnn of water in the pump, the boiler could supply the cylinder with steam, and 


that the engine would work regolarly with a moderate quantity of injection. It 
now appeared that the cylinder of the model being of brass, wonld conduct heat 
much better than the cast-iron cylinders of larger engines (generally covered on the 
inside with a stony crust), and that considerable advantage could be gained by TniiViTig 
the cylinders of some substance that would receive and give out heat slowly : of these, 
wood seemed to be the most likely, provided it should prove sufficiently durable. 

A small engine was therefore constructed with a cylinder six inches diameter, 
and twelve inches stroke, made of wood, soaked in linseed oil, and baked to dryness. 
With this engine many experiments were made ; but it was soon found that the 
wooden cylinder was not likely to prove durable, and that the steam condensed in 
filling it still exceeded the proportion of that required for large engines according to 
the statements of Desaguliers. It was also found, that all attempts to produce a 
better exhaustion by throwing in more injection, caused a disproportionate waste of 
steam. On reflection, the cause of this seemed to be the boiling of water in vacuo 
at low heats, a discovery lately made by Dr Cullen, and some other philosophers 
(below 100^, as I was then informed), and, consequently, at greater heats, the water 
in the cylinder would produce a steam which would, in part, resist the pressure of 
the atmosphere. 

By experiments which I then tried upon the heats at which water boils under 
several pressures greater than that of the atmosphere, it appeared, that when the 
heats proceeded in an arithmetical, the elasticities proceeded in some geometrical 
ratio ; and by laying down a curve from my data, I ascertained the particular one 
near enough for my purpose. It also appeared, that any approach to a vacuum 
could only be obtained by throwing in large quantities of injection, which would cool 
the cylinder so much as to require quantities of steam to heat it again, out of 
proportion to the power gained by the more perfect vacuum ; and that the old 
engineers had acted wisely in contenting themselves with loading the engine with 
only six or seven pounds on each square inch of the area of the piston. 

It being evident that there was a great error in Dr Desagulier's calculations of 
Mr Beighton*s experiments on the bulk of steam, a Florence flask, capable of 
containing about a pound of water, had about one ounce of distilled water put into 
it ; a glass tube was fitted into its mouth, and the joining made tight by lapping 
that part of the tube with packthread covered with glazier's putty. When the 
flask was set upright, the tube reached down near to the surface of the water, and in 
that position the whole was placed in a tin reflecting oven before a fire, until the 
water was wholly evaporated, which happened in about an hour, and might have 
been done sooner bad I not wished the heat not much to exceed that of boiling 
water. As the air in the flask was heavier than the steam, the latter ascended to 
the top, and expelled the sir through the tube. 

When the water was all evaporated, the oven and flask were removed from the 
fire, and a blast of cold air was directed against one side of the flask, to collect the 
condensed steam in one place. When all was cold, the tube was removed, the flask 
and its contents were weighed with care; and the flask being made hot, it was 
dried by blowing into it by bellows, and when weighed again, was found to have lost 
rather more than four grains, estimated at 4^ grains. 

When the flask was filled with water, it was found to contain about n\ ounces 
avoirdupois of that fluid, which gave about 1800 for the expansion of water converted 
into steam of the heat of boiling water. 

This experiment was repeated with nearly the same result; and in order to 
ascertain whether the flask had been wholly filled with steam, a similar quantity of 
water was for the third time evaporated ; and, while the flask was still cold, it was 


plaoed inverted, with its mouth (contracted by the tube) immersed in a vessel of 
water, which it sucked in as it cooled, until in the temperature of the atmosphere it 
was filled to within half-an-ounce measure of water. [In the contrivance of this 
•experiment, I was assisted by Dr Black. In Dr Bobison's edition of Dr Black's 
lectures, Vol. I. page 147, the latter hints at some experiments upon this subject 
A8 made by him; but I have no knowledge of any except those which I made 

In repetitions of this experiment at a later date, I simplified the apparatus by 
-omitting the tube, and laying the flask upon its side in the oven, partly closing 
its mouth by a cork having a notch on one side, and otherwise proceeding as has 
been mentioned. I do not consider these experiments as extremely accurate, the 
only scale-beam of a proper size which I had then at my command not being very 
sensible, and the bulk of the steam being liable to be influenced by the heat to 
which it is exposed, which, in the way described, is not easily regulated or ascer- 
tained ; but, from my experience in actual practice, I esteem the expansion to be 
rather more than I have computed. 

A boiler was constructed which showed, by inspection, the quantity of water 
•evaporated in any given time, and thereby ascertained the quantity of steam used 
in every stroke by the engine, which I found to be several times the full of the 
cylinder. Astonished at the quantity of water required for the injection, and the 
great heat it had acquired from the small quantity of water in the form of steam 
which had been used in filling the cylinder, and thinking I had made some mistake, 
the following experiment was tried : — A glass tube was bent at right angles, one end 
was inserted horizontally into the spout of a tea-kettle, and the other part was 
immersed perpendicularly in well-water contained in a cylindric glass vessel, and 
steam was made to pass through it until it ceased to be condensed, and the water in 
the glass vessel was become nearly boiling hot. The water in the glass vessel was 
then found to have gained an addition of about one-sixth part from the condensed 
steam. Consequently, water converted into steam can heat about six times its own 
weight of well-water to 212°, or till it can condense no more steam. Being struck 
with this remarkable fact, and not understanding the reason of it, I mentioned it to 
my Mend Dr Black, who then explained to me his doctrine of latent heat, which he 
had taught for some time before this period (summer 1764), but having myself 
been occupied with the pursuits of business, if I had heard it I had not attended to 
it, when I thus stumbled upon one of the material facts by which that beautiful 
theory is supported. 

On reflecting ftirther, I perceived, that in order to make the best use of steam, it 
was necessary, first, that the cylinder should be maintained always as hot as the 
steam which entered it; and secondly, that when the steam was condensed, the 
water of which it was composed, and the injection itself, should be cooled down to 
100°, or lower, where that was possible. The means of accomplishing these points 
did not immediately present themselves ; but early in 1765 it occurred to me, that 
if a communication were opened between a cylinder containing steam, and another 
Tcssel which was exhausted of air and other fluids, the steam, as an elastic fluid, 
would immediately rush into the empty vessel, and continue so to do until it had 
•established an equilibrium ; and if that vessel were kept very cool by an injection 
•or otherwise, more steam would continue to enter until the whole was condensed. 
But both the vessels being exhausted, or nearly so, how was the injection water, the 
Air which would enter with it, and the condensed steam, to be got out? 

This I proposed, in my own mind, to perform in two ways. One was by 
adapting to the second vessel a pipe reaching downwards more than 34 feet, by 

E. 2 


whieh the water would descend (a ooliiiim of that length over4ia1anmng the 
atmosphere), and bj eztraoting the air by means of a pomp. 

The second method was bj employing a pomp, or pomps, to extract both the air 
and the water, which woold be applicable in all places, and essential in those oases 
where there was no well or pit. 

This latter method was the one I then preferred, and is the only one I affcerwarda 
continued to use. In Newcomen's engine, the piston is kept tight by water, which 
coold not be applicable in this new method ; as, if any of it entered into a partially 
exhaosted and hot cylinder, it woold boil and present the production of a vacuom^ 
and woold also cool the cylinder, by its eyaporation doring the descent of the 

I proposed to remedy this defect by employing wax, tallow, or other grease, to 
lobricate and keep the piston tight. It next occorred to me, that the mouth of the 
cylinder being open, the air which entered to act on the piston would cool the 
cylinder, and condense some steam on again filling it, I therefore proposed to put an 
air-tight cover upon the cylinder, with a hole and stuffing-box for the piston-rod to 
slide through and to admit steam above the piston to act upon it instead of the 
atmosphere. [N.B. The piston-rod sliding through a stuffing-box was new in steam- 
engines ; it was not necessary in Newoomen's engine, as the mouth of the cylinder 
was open, and the piston stem was square and veiy clumsy. The fitting the piston- 
rod to the piston by a cone was an after improvement of mine (about 1774).] There 
still remained another source of the destruction of steam, the cooling of the cylinder 
by the external air, which would produce an internal condensation whenever steam 
entered it, and which would be repeated every stroke ; this I proposed to remedy by 
an external cylinder containing steam, surrounded by another of wood, or of some 
other substance which would conduct heat slowly. 

When once the idea of the separate condensation was started, all these improve- 
ments followed as corollaries in quick succession, so that in the course of one or two 
dajrs, the invention wm thus far complete in my mind, and I immediately set about 
an experiment to verify it practically. I took a large brass syringe. If inches 
diameter, and 10 inches long, made a cover and bottom to it of tin-plate, with & 
pipe to convey steam to both ends of the cylinder from the boiler; another pipe to 
conv^ steam from the upper end to the condenser (for, to save apparatus, I inverted 
the cylinder). I drilled a hole longitudinaUy through the axis of the stem of the 
piston, and fixed a valve at its lower end, to permit the water which was produced 
by the condensed steam on first filling the cylinder, to issue. The condenser used 
upon this occasion consisted of two pipes of thin tin-plate, ten or twelve inches long, 
and about one-sixth inch diameter, standing perpendicular, and communicating at 
top with a short horizontal pipe of large diameter, having an aperture on its upper 
side which was shut by a valve opening upwards. These pipes were joined at 
bottom to another perpendicular pipe of about an inch diameter, which served for 
the air and water-pump ; and both the condensing pipes and the air-pump were 
placed in a small cistern filled with cold water. [N.B. This construction of the 
condenser was employed from knowing that heat penetrated thin plates of metal 
very quickly, and considering that if no injection was thrown into an exhausted 
vessel, there would be only the water of which the steam had been composed, and 
the air which entered with the steam, or through the leaks, to extract.] 

The steam-pipe was adjusted to a small boiler. When steam was produced, it 
was admitted into the cylinder, and soon issued through the perforation of the rod, 
and at the valve of the condenser. When it was judged that the air was expelled, 
the steam-cock was shut, and the air-pump piston-rod was drawn up, which leaving 


the small pipes of the condenser in a state of vaonmn, the steam entered them and 
was condensed. The piston of the cylinder immediately rose and lifted a weight of 
about 18 lbs., which was hong to the lower end of the piston-rod. The exhaustion- 
cock was shut, the steam was readmitted into the cylinder, and the operation was 
repeated, the quantity of steam consumed, and the weights it conla raise were 
observed, and, excepting the non-application of the steam-case and external covering, 
the invention was complete, in so far as regarded the savings of steam and fuel. 

A large model, with an outer cylinder and wooden case, was immediately con- 
structed, and the experiments made with it served to verify the expectations I had 
formed, and to place the advantage of the invention beyond the reach of doubt. It 
was found convenient afterwards to change the pipe-condenser for an empty vessel, 
generally of a cylindrical form, into which an injection played, and in consequence 
of there being more water and air to extract, to enlarge the air-pump. 

The change was made, because, in order to procure a surface sufficiently extensive 
to condense the steam of a large engine, the pipe-condenser would require to be very 
voluminous, and because the bad water with which engines are frequently supplied, 
would crust over the thin plates, and prevent their conveying the heat sufficiently 
quick. The cylinders were also placed with their mouths upwards, and furnished 
with a working-beam and other apparatus as was usual in the ancient engines ; the 
inversion of the cylinder, or rather of the piston-rod, in the model, being only an 
expedient to try more easily the new invention, and being subject to many objections 
in large engines." 

13. Development of Watt's Engine: the rotative 
type. In a second patent (1781) Watt describes the "sun-and- 
planet'' wheels and other methods of making the engine give 
continuous revolving motion to a shaft provided with a fly-wheel. 
He had intended to use the crank and connecting-rod, for this 
purpose (a mechanical device familiar even at that time from its 
use in the common foot-lathe), and had even made a model of it, 
but the application of the crank to the steam-engine had mean- 
while been patented by one Pickard, and Watt, rather than make 
terms with Pickard, made use of his sun-and-planet motion until 
the patent for the application of the crank expired. The re- 
ciprocrating motion of earlier forms had served only for pumping, 
but by this invention Watt opened up for the steam-engine a 
thousand other channels of usefulness. The engine was still 
single-acting ; the connecting rod was attached to the far end of 
the beam, and that carried a counterpoise which served to raise 
the piston when steam was admitted below it. 

14. Further improvements by Watt. In 1782 Watt 
patented two further improvements of the first importance, both 
of which he had invented some years before. One was the use of 
double action, that is to say, the application of steam and vacuum 
to each side of the piston alternately. The other, which had 




been invented as early as 1769, was the use of steam expansively, 
in other words the plan (now used in all engines that aim at 

Fig. 7.— Watt's Double-acting Engine, 1782. 

economy of fuel) of stopping the admission of steam when the 
piston had made only a part of its stroke, and allowing the rest 
of the stroke to be performed by the expansion of the steam 
already in the cylinder. To let the piston push as well as pull 
the end of the beam Watt devised his so-called parallel motion, 
an arrangement of links connecting the piston-rod head with the 
beam in such a way as to guide the rod to move in a very nearly 


straight line. He further added the throttle-valve, for regulating 
the rate of admission of steam, and the centrifugal governor, a 
double conical pendulum, which controlled the speed by acting 
on the throttle-valve. The stage of development reached at this 
time is illustrated by the engine of fig. 7 (from Stuart's History 
of the Steam-engine), which shows the parallel motion pp, the 
governor g, the throttle-valve t, and a pair of steam and exhaust 
valves at each end of the cylinder. 

Among other inventions of Watt were , the " indicator," by 
iw^hich diagrams showing the relation of the steam-pressure in 
the cylinder to the movement of the piston are automatically 
drawn; a steam tilt-hammer; and also a steam locomotive for 
ordinary roads, — ^but this invention was not prosecuted. As an 
inventor Watt was skilfully seconded by his assistant Murdoch, 
to whose ingenuity, he says, are due "many improvements" — 
amongst them, the introduction of the slide-valve as a means of 
controlling the admission and release of steam. 

In partnership with Matthew Boulton, Watt carried on in 
Birmingham the manufacture and sale of his engines with the 
utmost success, and held the field against all rivals in spite of 
severe assaults on the validity of his patents. A special Act of 
Parliament was obtained which extended the patent monopoly for 
a term of twenty-five years from 1775. Notwithstanding Watt's 
knowledge of the advantage to be gained by using steam expan- 
sively he continued to employ only low pressures — seldom more 
than 7 lbs. per square inch over that of the atmosphere. His 
boilers were fed, as Newcomen's had been, through an open pipe 
which rose high enough to let the column of water in it balance 
the pressure of the steam. Following Savery, he adopted the 
term " horse-power " as a mode of rating engines and gave it a 
particular meaning, by defining one horse-power as the rate at 
which work is done when 33,000 lbs. are raised one foot in one 
minute. This estimate was based on trials of the work done by 
horses ; it is excessive as a statement of what an average horse 
can do, but Watt purposely made it so in order that .his customers 
might have no reason to complain on this score. 

16. Non-condensing Steam-Bngines. In the fourth 
claim in Watt's first patent, the second sentence describes a non- 
condensing engine, which would have required steam of a con- 



siderably higher pressure than served in the condensing engine. 
His narrative also shows that he had made experiments in 
this direction before devising the separate condenser. This, 
however, was a line of invention which Watt did not follow up, 
perhaps because so early as 1725 a non-condensing engine had 
been described by Leupold in his Theatrum Majchinamnu 
Leupold's proposed engine (for the main features of which he 
professes himself indebted to Papin) is shown in fig. 8, which 


Fig. 8. Non-condensing Engine described by Leupold (1725). 

makes its action sufficiently clear. Watt's aversion to high- 
pressure steam was strong, and its influence on steam-engine 
practice long survived the expiry of his patents. So much indeed- 
was this the case that the terms "high-pressure" and "non- 
condensing" were for many years synonjrmous, in contradis- 
tinction to the "low-pressure" or condensing engines of Watt. 
This nomenclature no longer holds good; in modem practice 
many condensing engines use as high pressures as non-con- 


densing engines, and by doing so are able to take advantage of 
Watt's great invention of expansive working to a degree which 
was impossible in his own practice. 

16. Use of comparatlTely high-pressure steam. The 

introduction of the non-condensing and, at that time, relatively 
high-pressure engine was effected in England by Trevithick and 
in America by Oliver Evans about 1800. Both Evans and 
Trevithick applied their engines to propel carriages on roads, and 
both used for boiler a cylindrical vessel with a cylindrical flue 
inside — the construction now known as the Cornish boiler. In 
partnership with Bull, who had been a workman in the employment 
of Boulton and Watt, Trevithick had previously made direct- 
acting pumping-engines, with an inverted cylinder set over and in 
line with the pump-rod, thus dispensing with the beam that had 
been a feature in all earlier forms. But in these " Bull " engines, 
as they are called, a condenser was used, or, rather, the steam was 
condensed by a jet of cold water in the exhaust-pipe, and Boulton 
and Watt successfully opposed them as infringing the patent for 
condensation in a separate vessel. To Trevithick belongs the 
distinguished honour of being the first to use a steam-carriage on 
a railway ; in 1804 he built a locomotive in the modem sense, to 
run on what had formerly been a horse-tramway in Wales ; and it 
is noteworthy that the exhaust steam was discharged into the 
funnel to force the furnace draught, a device which, 25 years later, 
in the hands of George Stephenson, went far to make the loco- 
motive what it is to-day. In this connexion it may be added that 
as early as 1769 a steam-carriage for roads had been built in 
France by Cugnot, who used a pair of single-acting high-pressure 
cylinders to turn a driving axle step by step by means of pawls 
and ratchet-wheels. To the initiative of Evans may be ascribed 
the early general use of high-pressure steam in the United States, 
a feature which for many years distinguished American from 
English practice. 

17. Compound Engines. Homblower and WoolC A- 

mongst the contemporaries of Watt one name deserves special 
mention. In 1781 Jonathan Homblower constructed and patented 
what would now be called a compound engine, with two cylinders 
of different sizes. Steam was first admitted into the smaller 
cylinder, and then passed over into the larger, doing work against 


a piston in each. In Homblower's engine the two cylinders were 
placed side by side, and both pistons acted on the same end of a 
beam overhead. This was an instance of the use of steam ex- 
pansively, and as such was earlier than the patent, though not 
earlier than the invention, of expansive working by Watt. Horn- 
blower was crushed by the Birmingham firm for infringing their 
patent in the use of a separate condenser and air-pump. 

Soon after the expiry of Watt's master patent in 1800 the com- 
pound engine was revived by Woolf, with whose name it is often 
associated. Using steam of fairly high pressure, and cutting off 
the supply before the end of the stroke in the small cylinder, 
Woolf expanded the steam to six or even nine times its original 
volume. Mechanically the double-cylinder compound engine has 
this advantage over an engine in which the same amount of 
expansion is performed in a single cylinder, that the thrust or 
pull exerted by the two pistons in the compound engine varies 
less throughout the action than that which is exerted by the piston 
of the single-cylinder engine. This advantage may have been clear 
to Hornblower and Woolf, and to other early users of compound 
expansion. But another and a more important merit of the 
system lies in a fact of which neither they nor for many years 
their followers in the use of compound engines were aware — the 
fact that by dividing the whole range of expansion into two parts 
the cylinders in which these are separately performed are subject 
to a reduced range of fluctuation in their temperature. This, as 
we shall have occasion to point out more particularly in a later 
chapter, limits to a great extent a source of waste which is present 
in all steam-engines, namely, the waste which results from the 
heating and cooling of the metal by its alternate contact with hot 
and cooler steam. The system of compound expansion is now 
used in nearly all large engines that pretend to economy. Its 
introduction forms the only great improvement which the steam- 
engine has undergone since the time of Watt ; and we are now 
able to recognize it as a very important step in the direction set 
forth in his " first principle," that the cylinder should be kept as 
hot as the steam that enters it. 

18. The Oomiih Pumping Engine. Woolf introduced 
the compound engine somewhat widely about 1814, as a pumping 
engine in the mines of Cornwall. But it met a strong competitor 


there in the high-pressure single-cylinder condensing engine, 
which was at that time developing, in the hands of Trevithick 
and others into a machine of great efficiency, and which had 
an evident advantage over Woolf s in the simplicity of its con- 
struction. Woolfs engine fell into comparative disuse, and the 
single-cylinder type took a form which, under the name of the 
Cornish pumping engine, was for many years famous for its great 
economy of fuel. In this engine the cylinder was set under one 
end of a beam, from the other end of which hung a heavy rod 
which operated a pump at the foot of the shaft. Steam was 
admitted above the piston for a short portion of the stroke, there- 
by raising the pump-rod, and was allowed to expand for the 
remainder. Then an equilibrium valve, connecting the spaces 
above and below the piston, as in fig. 6, was opened, and the 
pump-rod descended, doing work in the pump and raising the 
engine piston. The large mass which had to be started and 
stopped at each stroke served by its inertia to counterbalance the 
inequalities of steam pressure which were due to expansive 
working, for the pump rods and other reciprocating parts stored 
up energy of motion in the early part of the stroke, when the 
steam pressure was greatest, and gave out energy in the later part, 
when expansion had greatly lowered the pressure. The frequency 
of the stroke was controlled by a device called a cataract, con- 
sisting of a small plunger pump, in which the plunger, raised at 
each stroke by the engine, was allowed to descend more or less 
slowly by the escape of fluid below it through an adjustable 
orifice, and in its descent liberated catches which held the steam 
and exhaust valves from opening. A similar device controlled the 
equilibrium valve. The cataract could be set to give a pause at 
the end of the piston's down-stroke, so that the pump cylinder 
might have time to become completely filled. 

The Cornish engine is interesting as the earliest form which 
achieved an efficiency at all comparable with that of good modem 
engines. For many years monthly reports were published of the 
" duty " of these engines, the " duty " being the number of foot- 
pounds of work done per bushel or (in some cases) per cwt. of 
coal. The performance of the engines became a matter of almost 
sporting interest to mining engineers, and no pains were spared 
to "beat the record." The average duty of engines in the 
Cornwall district rose from about 18 millions of foot-pounds 


per cwt. of coal in 1813 to 68 millions in 1844, after which 
less effort seems to have been made to maintain a high effi- 
ciency*. In individual cases much higher results were reported, 
as in the Fowey Consols engine, which in 1835 was stated to 
have a duty of 125 millions. This (to use a more modem 
mode of reckoning) is equivalent to the consumption of only 
a little more than If lb. of coal per hour per horse-power — a 
result surpassed by very few engines in even the best recent 
practice. It is difficult to credit figures which, even in exceptional 
instances, place the Cornish engine of that period on a level with 
the most efficient modern engines — ^in which compound expansion 
and higher pressure combine to make a much more perfect 
thermodynamic machine; and apart from this there is room to 
question the accuracy of the Cornish reports. They played, how- 
ever, a useful part in the process of steam-engine development by 
directing attention to the question of efficiency, and by demon- 
strating the advantage to be gained frx)m high-pressure and 
expansive working, at a time when the theory of the steam-engine 
had not yet taken shape. 

It may be added that the success of the Cornish type was no 
doubt largely responsible for the tendency which down to a very 
recent period engine builders have shown to interpose a beam 
between the steam-cylinder and the pump or crank on which work 
is being done. For a long time the beam appears, in one form or 
another, as an almost inevitable part of a steam-engine. The 
lesson to be learnt from Bull's early direct-acting engine was 
apparently, in general, overlooked. 

19. Revival of the Compound Engine. The final revival 
of the compound engine did not occur until about the middle of 
the century, and then several agencies combined to bring it about. 
In 1845 M* Naught introduced a plan of improving beam engines 
of the original Watt type, by adding a small high-pressure cylinder 
with a piston acting on the beam between the centre and the fly- 
wheel end. Steam of higher pressure than had formerly been 
used, after doing work in the new cylinder, passed into the old or 
low-pressure cylinder, where it was further expanded. Many 
engines whose power was proving insufficient for the extended 
machinery they had to drive were "M*Naughted" in this way, 

1 Min, Proe. Inst C,E,, vol. xxiii., 1S63. 


and after conversion were found not only to exert more power but 
to show a marked economy of fuel. The compound form was 
selected by Mr Pole for the pumping engines of Lambeth and 
other waterworks about 1850 ; in 1854 John Elder began to use 
it in marine engines; in 1867 Mr E. A. Cowper added a steam- 
jacketed intermediate reservoir for steam between the high and 
low-pressure cylinders, which made it unnecessary for the low- 
pressure piston to be just beginning when the other piston was just 
ending its stroke. As the mechanical construction of engines and 
boilers improved and facilities therefore increased for the use of 
high-pressure steam, compound expansion became more and more 
general, its advantage becoming more conspicuous with every 
increase in boiler pressure. Now-a-days there are few large land 
engines and scarcely any marine engines that are not compound. 
In marine practice especially, where economy of fuel is a much 
more important factor in determining the design than it is on 
land, the principle of compound expansion has been greatly 
extended by the general introduction of triple and occasionally 
even of quadruple expansion engines, in which the steam is made 
to expand successively in three or in four cylinders. Even in 
locomotives for railways, where other considerations are of more 
moment than the saving of coal, the system of compound expansion 
has found a place, though its use there is by no means general. 

The growth of compound expansion has been referred to at 
some length, because it forms the most distinctive improvement 
which the steam-engine has undergone since the time of Watt. 
For the rest, the progress of the steam-engine has consisted in its 
adaptation to particular uses, in the invention of features of 
mechanical detail, in the recognition and application of thermo- 
dynamical principles, in better structural design and in improved 
methods of manufacture by which it has profited in common with 
all other machinea These have made possible the use of steam of 
eight or ten times the pressure of that employed by Watt, and 
have allowed the mean speed of movement of the piston to be 
greatly increased, with consequent gains both in the amount of 
power obtainable from an engine of given size and in the efficiency 
of the action. 

20. AppUcatioii to locomotives. The adaptation of the 
steam-engine to railways, begun by Trevithick, became a success 


in the hands of George Stephenson, whose engine the '' Bocket/' 
when tried along with others on the Stockton and Darlington 
road in 1829, not only distanced its competitors but settled once 
and for all the question whether horse traction or steam traction 
was to be used on railways. The principal features of the 
"Rocket" were an improved steam-blast for urging the combustion 
of coal and a boiler (suggested by Booth, the secretary of the rail- 
way) in which a large heating surface was given by the use of 
many small tubes through which the hot gases passed. Further, 
the cylinders, instead of being vertical as in earlier locomotives, 
were set at a slope, which was afterwards altered to a position 
still more nearly horizontal. To these features there was added 
later the "link motion," a contrivance which enabled the engine 
to be quickly reversed and the amount of expansion to be readily 
varied. In the hands of George Stephenson and his son Robert 
the locomotive took a form which has been in all essentials main- 
tained by the far heavier locomotives of modem practice. 

21. Application to iteamboats. The first practical steam- 
boat was the tug " Charlotte Dundas," built by William Syming- 
ton, and tried in the Forth and Clyde Canal in 1802. A Watt 
double-acting condensing engine, placed horizontally, acted directly 
by a connecting-rod on the crank of a shaft at the stem, which 
carried a revolving paddle-wheel. The trial was successful, but 
steam towing was abandoned for fear of injuring the banks of the 
canal. Ten years later Henry Bell built the " Comet," with side 
paddle-wheels, which ran as a passenger steamer on the Clyde; 
but an earlier inventor to follow up Symington's success was the 
American Robert Fulton, who, after unsuccessful experiments on 
the Seine, fitted a steamer on the Hudson in 1807 with engines 
made to his designs by Boulton and Watt, and brought steam 
navigation for the first time to commercial success. 

The American river boats soon began to use high-pressure 
steam, but English engineers looked askance on a practice which 
led to frequent explosions. They were moreover slow to realise 
that high pressure is a necessary condition of economical working. 
In 1835 it was usual for the pressure in marine boilers to be no 
more than 4 or 5 pounds per square inch above the pressure of 
the atmosphere, and for many years later pressures of 20 or 25 
pounds were common. With the introduction of compound 


working and with the substitution of cylindrical boilers for the 
weak box-boiler originally used on board ship the pressure rose 
considerably. In 1872 Sir F. Bramwell, describing the typical 
marine practice of that timeS gives a list of engines — all com- 
pound — in which the pressure ranged from 45 to 60 pounds. 
The consumption of coal in these engines was generally from 2 to 
2^ pounds per hour per indicated horse-power, and the mean 
piston speed was about 350 feet per minute. Nine years later 
Mr F. C. Marshall gives a similar list*, in which the mean pressure 
is 77 pounds, the mean piston speed about 460 feet per minute, 
and the consumption of coal a trifle under 2 pounds per hour per 
indicated horse-power. These engines were also of the type in 
which steam is successively expanded in two cylinders. The triple 
expansion type of engine came into general use shortly after that 
date and led at once to a marked advance in boiler pressure with 
a considerable gain in economy of fuel. Reviewing the progress 
of marine engineering in the decade from 1881 to 1891 Mr 
Blechynden' gives a list of triple engines with boiler pressures of 
about 160 pounds and piston speeds of about 500 or 600 feet per 
minute. These engines consume on the average about 1^ pounds 
of coal per indicated horse-power-hour. 

The remarkable efficiency now reached by the marine engine 
is in part due to its great size; a big engine being, cceteris paribus, 
rather more efficient than a small one. The rapid growth in size 
is a marked feature of recent progresa Ten thousand indicated 
horse-power as the performance of a single set of engines is not 
unusual in a first-rate Atlantic liner or in a war vessel The 
twin-screw engines of the "Paris" or of the "New York" de- 
velope together some twenty thousand horse-power. To take a 
still more recent instance the twin-engines of the Campania 
(1893) work at 31,000 horse-power, with a boiler pressure of 
165 pounds per square inch and a mean piston speed of about 
1000 feet per minute. We shall have occasion in later chapters 
to mention some of the forms which the steam-engine has 
assumed in present day practice, and to state more particularly 
the results which have been found in trials made to determine 
the efficiency. 

1 Proe. Inst, Meek, Eng,, 1872. 
* Proe, Irut, Mech. Eng,, 1881. 
» Proe, Inst, Meek. Eng,, 1891. 


22. Development of the Theory of Heat-Xnglnee. It 

is remarkable how little the infiemcy of the steam-engine has owed 
to scientific nursing. The early inventors had no theory of 
thermodynamics to guide them. Watt had the advantage, as 
he mentions in his narrative, of a knowledge of Black's doctrine 
of latent heat; but there was no philosophy of the relation of 
work to heat until long after the inventions of Watt were com- 
plete. The theory of the steam-engine as a heat-engine may be 
said to date fix>m 1824, when Camot published his Biflexions sur 
la Puissance Motrice du Feu. He there showed that heat does 
work only by being let down from a higher to a lower temperature. 
But Camot had no idea that any of the heat disappears in the 
process, and it was not until the doctrine of the conservation of 
energy was established in 1843 by the experiments of Joule, which 
determined the mechanical equivalent of heat, that the theory 
of heat-engines began a vigorous growth. Important data were 
furnished by Begnault's classical experiments on the properties 
of steam, the results of which were published in 1847. From 1849 
onwards the science of thermodynamics was developed with extra- 
ordinary rapidity by Clausius, Rankine, and Thomson (Lord Kelvin), 
and was applied, especially by Rankine, to practical problems in 
the use of steam. The publication in 1859 of Bankine's Manual 
of the Steam-Engine formed an epoch in the philosophical treat- 
ment of the subject and gave steam engineers the opportunity 
of ceasing to be mere empirics. Unfortunately, however, for its 
bearing on practice, while the thermodynamic theory was rigorous 
in itself, the application of it to steam-engine problems was to a 
great extent founded on certain simplifying assumptions which 
experience has since shown to be far from correct. It was 
assumed that the cylinder and piston might be treated aa be- 
having to the steam like non-conducting bodies, — that the 
transfer of heat between the steam and the metal was negligibly 
small. Rankine's calculations of steam-consumption, of work, 
and of thermodynamic efficiency involve this assumption, except 
in the case of steam-jacketed cylinders, where he estimates 
that the steam in its passage through the cylinder takes just 
enough heat from the jacket to prevent a small amount of con- 
densation which would otherwise occur as the process of expansion 
goes on. These assumptions are not supported by experiment. 
If the transfer of heat from steam to metal could be overlooked. 


the steam which enters the cylinder would remain during ad- 
n^LBsion as dry as it was before it entered, and the volume of 
steam consumed per stroke would correspond with the volume of 
the cylinder up to the point of cut-off. It is here that the actual 
behaviour of steam in the cylinder diverges most widely from the 
behaviour which has been assumed. When steam enters the 
cylinder it :finds the metal chilled by the previous exhaust, and a 
portion of it is at once condensed. This has the effect of in- 
creasing, often very largely, the volume of boiler steam required 
per stroke. As expansion goes on the water that was condensed 
during admission begins to be re-evaporated from the sides of the 
cylinder, and this action is generally continued during the escape 
of the steam. In later chapters the effect which this exchange of 
heat between the metal of the cylinder and the working fluid 
produces on the economy of the engine will be discussed, and an 
account will be given of experimental means by which we may 
examine the amount of steam that is initially condensed and trace 
its subsequent re-evaporation. The influence which the walls of 
the cylinder exert is in fact immense, by the alternate give and 
take of heat between them and the steam. It is now recognized 
that any theory which fails to take account of these exchanges of 
heat fails also to yield even comparatively correct results in cal- 
culating the relative eflSciency of various steam pressures or various 
ranges of expansion. But the exchanges of heat are so complex 
that there seems little prospect of submitting them to any com- 
prehensive theoretical treatment, and we must rather look for 
help in the future development of engines to the scientific analysis 
of experiments made upon actual machines. Many such experi- 
ments have been made and their value is now fully realised, by no 
persons more than by the designers of the best modem engines. 
Questions relating to the influence on thermal economy of speed, 
of pressure, of ratio of expansion, of jacketing, of compound 
expansion, or of superheating must in the main be settled by an 
appeal to experiment. The student must not, however, conclude 
that because the conditions under which an actual engine works 
are so complex as to make an exact theory of the action im- 
practicable, no theory need be studied. The very complexity of 
conditions makes the study of theory more necessary, as a guide in 
judging what conditions are favourable to eflBciency and what are 
unfavourable. Moreover the general theory of heat-engines gives 


the steam engineer a counsel of perfection, by assigning a limit of 
efficiency which engines may approach but cannot surpasa Even 
to interpret rightly the results of experiments requires a know- 
ledge both of the principles of thermodynamics and of the physical 
properties of steam. 

Refereneet, — ^Diroks, Life of the Marquis of Worcester, 1865, oontaining a reprint 
of the Century of Inventions (1663). Desaguliers, Course of Experimental Philo- 
sophy, 1763. BobiBon, System of Mechanical Philosophy, Vol. ii. 1822. Staart, 
Descriptive History of the Steam-Engine, 1825 ; Farey, Treatise on the Steam-Engine, 
1827; Tredgold, The Steam-Engine, 1838; Muirhead, Mechanical Inventions of 
Jam£s Watt, and Life of Watt ; GaUoway, The Steam-Engine and its Inventors ; 
Thorston, History of the Growth of the SUam-Engine ; Gowper on the Steam-Engine 
{Heat Lectures, Inst, C.E„ 1884.) 



23. Laws of Thermodynamics. The First Law. In the 

action of a heat-engine, heat is either taken in by the engine from 
a furnace or from some external source or is generated by the com- 
bustion of fuel within the engine itself. A portion of the heat thus 
supplied is spent in doing mechanical work and so ceases to exist 
as heat, being converted into another form of energy; and the 
remainder is rejected by the engine, still in the form of heat. The 
i;plation which holds between the heat supplied, the heat converted 
into mechanical energy, and the heat rejected depends on two 
general principles which are described as the two Laws of Thermo- 
dynamics. . The first law states the fact that the amount of heat 
which disappears in the process (as heat) is proportional to the 
amount of mechanical work done in the engine ; in other words 
it states the principle of the Conservation of Energy in relation to 
the doing of mechanical work by the agency of heat. This may 
be expressed in the following terms: — When Tnechaniccd energy 
%8 produced from heat a definite quantity of heat goes out of 
existence for every unit of work done; and conversely , when 
heat is produced by the expenditure of mechanical energy Ike same 
definite quantity of heat comes into existence for every unit of 
work spent. 

To put this statement into a numerical form we must have a 
unit for the measurement of quantities of heat as well as a unit 
for the measurement of mechanical work. For engineering purposes 
the foot-pound is the common unit of work. This convenient and 
fitmiliar unit is open to the objection that it has slightly different 
values in different places on account of differences in the intensity 
£. 3 


of gravity ; but these differences are scarcely large enough to be 
important firom a practical point of view. In cases where greater 
precision of statement is required a particular locality or rather a 
particular latitude has to be specified, or recourse may be had to 
absolute units, such as the foot-poundal or the erg, which are 
independent of gravity. 

Quantities of heat are expressed in terms of the ihermal unk^ 
which is the quantity of heat required to raise the temperature of 
1 lb. of water by I degree. Fahrenheit's scale is generally used by 
English engineers in stating temperature, and so the Fahrenheit 
degree is to be understood in this definition. The corresponding 
unit of heat on the Centigrade mode of reckoning would be greater 
in the proportion of nine to fiva To make the definition of the 
thermal unit precise we have to specify at what place in the scale 
of temperature the change through one degree is supposed to 
occur, for the specific heat of water is not quite constant. It 
takes rather more heat to raise the temperature of a pound of water 
1 degree if the temperature is high than if it is low. By Bankine 
and others the standard temperature assumed in the definition 
is that of the maximum density of water, or about 39® Fah. : later 
writers have preferred to take a standard temperature of about 
60® Fah., but the difference is scarcely material. 

Our knowledge of the mechanical equivalent of heat is origin- 
ally due to the experiments of Joule, which were begun in 1843 
and continued for many years. Causing the potential energy of a 
raised weight to be spent in turning a paddle which generated 
heat by the agitation of the liquid in which it was immersed and 
observing the increase in temperature which this brought about. 
Joule arrived at the figure 772 as the number of foot-pounds 
equivalent to one thermal (Fahrenheit) unit, and this was for long 
the commonly accepted value of the mechanical equivalent of heat. 
Later experiments by Joule himself gave a larger number ; in 
1878 an improved method of measurement, in which the mechani- 
cal stirring of water was still used, pointed to a value between 
774 and 775. A comparison by Rowland* of the scale of the 
thermometer used by Joule with that of an air thermometer led 
to a further increase in this number, bringing it to about 778, 
and this value has received confirmation from the experiments 

^ Proceedings of the American Academy, 1879. 


of Rowland himself and more recently from those of QriiSSths^ 
which were conducted by entirely different methods. Taking 
the evidence together, there can be no doubt that the old number 
is too low, and that the true value of the mechanical equivalent 
of one thermal unit is at least 778 and perhaps as much 
as 779 foot-pounds. The number 778 is used in the calculations 
that occur in this booL Since a definite number of foot-pounds 
is equivalent to 1 thermal unit, we may, if we please, express 
quantities of work in thermal units, or quantities of heat in foot- 

24. The Second Law of ThermodynamicB. It is im- 
possible for a Self-acting machine, unaided by any external agency, 
to convey heat from one body to another at a higher temperature. 

This is the form in which the second law has been stated by 
Clausius^ Another statement of it, different in form but similar 
in effect, has been given by Lord Kelvin*. Its force may not be 
immediately obvious, but it will be shown below that this law sets 
a most important limit to the convertibility of heat into work. 
So far as the first law goes, there is nothing to prevent the 
whole heat taken in by an engine from changing into mechanical 
energy. In consequence of the second law, however, as we shall 
presently see, no heat-engine converts, or can convert, more than 
a small fraction of the heat supplied to it into work ; a large part 
is necessarily rejected as heat. The ratio 

Heat converted into work 
Heat taken in by the engine 

is a fraction always much less than unity. This fraction is called 
the efficiency of the engine considered as a heat-engine. 

26. The Working Substance in a Heat-Engine. In 

every heat-engine there is a working substance which alternately 
takes in and rejects heat. In general it suffers changes of volume, 
and does work by overcoming resistance to these changes. The 
working substance may be gaseous, liquid, or solid. We can, for 
example, imagine a heat-engine in which the working substance 

1 PhU. Trans. Roy. 8oc. 1893. 

^ See GlausiuB' Mechanical Theory of Heat, translated by W. B. Browne. 
* See Lord Eelvin's (Sir W. Thomson's) CoUecUd Papert, Vol. z., for his early 
investigations in thermodynamic theory. 



ifl a long metallic rod, arranged to act as the pawl of a ratchet- 
wheel with closely pitched teeth. Let the rod be heated so that 
it elongates sufficiently to drive the wheel forward through the 
space of one tootk Then let the rod be cooled (say by applying 
cold water), the ratchet-wheel being meanwhile held from return- 
ing by a separate click or detent. The rod, on cooling, will retract 
so as to engage itself with the next succeeding tooth, which may 
then be driven forward by heating the rod again, and so on. To 
make it evident that such an engine would do work, we have only 
to suppose that the ratchet-wheel carries round with it a drum by 
which a weight is wound up. The device forms a complete heat- 
engine, in which the working substance is a solid rod, which 
receives heat by being brought into contact with some source of 
heat at a comparatively high temperature, transforms a small part 
of this heat into work, and rejects the remainder to what we may 
call a receiver of heat, at a comparatively low temperature. The 
greater part of the heat may be said simply to pass through the 
engine, from the source to the receiver, becoming degraded aa 
regards temperature as it goes. It will be seen presently that 
this is typical of the action of all heat-engines ; when they are 
doing work they must take in heat at a comparatively high 
temperature and reject heat at a comparatively low temperature. 
They convert some heat into work only by letting down a much 
larger quantity of heat from a high to a relatively low tempera- 
ture. The action is, to some extent, analogous to that of a 
water-wheel, which does work by letting down water from a high 
to a lower level, change of level in the one case being the analogue 
of change of temperature in the other. But there is this important 
diflference, that whereas in the action of the water-wheel none 
of the water disappears, in the action of the heat-engine an 
amount of heat disappears which is equivalent to the work done. 

26. Graphic Representation of Work done in the 
changes of volume of a fluid. In almost all actual heat-engines 
the working substance is a fluid. In some it is air, in some a 
mixture of several gasea In the steam-engine the working fluid 
is a mixture (in varying proportions) of water and steam. With a 
fluid for working substance, work is done by changes of volume 
only; its amount depends solely on the relation of pressure to 
volume during the change, and not at all on the form of the vessels 




liich the change takes place. Let a diagram be drawn (fig. 9) 
in which the relation of the intensity of pressure to the volume of 
any ^upposed working fluid is graphically exhibited by the line 

', where AM, GN are pressures and AP, CQ are volumes, then 
the work done by the substance in expanding from volume AP to 
volume CQ is the area of the figure MABGN, And similarly, if the 
substance be compressed from volume CQ back to its original volume 
in such a manner that the line CD A represents the relation of pres- 
sure and volume during compression, a quantity of work is done upon 
the substance which is represented by the area NOD AM. Taking 
the two operations together, we find that the substance has done a 

net amount of work equal to the area of the shaded figure ABGDA, 
or JPdV, This is an example and a generalization of the method 
of representing work which Watt introduced by his invention of 
the indicator ; the figure ABGDA may be called the indicator did- 
gram of the supposed action. 

27. Cycle of operations of the working subitance. 

Modern forms of the indicator will be described in a later chapter. 
For the present it may suffice to say that the indicator draws 
automatically a diagram showing the relation of the pressure of 
the working fluid to the movement of the piston, or in other words 
to the volume of working fluid in the cylinder, and thus gives 
complete information as to the work done throughout the stroke. 
Generally in heat-engines the working substance returns periodi- 
cally to the same state of temperature, pressure, volume, and 
physical condition. Each time this has occurred the substance is 
said to have passed through a complete cycle of operationa For 
example, in a condensing steam-engine, water taken trom the hot- 


well is pumped into the boiler ; it then passes into the cylinder as 
steam, passes thence into the condenser, and thence again as water 
into the hot-well ; it completes the cycle by returning to the same 
condition as at first. In other less obvious cases, as in that of the 
non-condensing steam-engine, a little consideration will show that 
the cycle is completed, not indeed by the same portion of working 
substance being returned to the boiler, but by an equal quantity 
of water being fed to it, while the steam which has been discharged 
into the atmosphere cools to the temperature of the feed-water. In 
the theory of heat-engines it is of the first importance to consider 
as a whole the cycle of operations 'performed by the working 
substance (as was first done by Camot in 1824). If we stop short 
of the completion of a cycle matters are complicated by the fact 
that the substance is in a state different from its initial state, 
and may therefore have changed its stock of internal energy. 
After the cycle is completed, on the other hand, the internal energy 
of the substance is necessarily the same as at first, since the con- 
dition is in every respect the same. Hence in regard to the cyclic 
process as a whole this equation must hold good, 

Heat taken in = work done + heat rejected. 

28. Engine using a perfect gas as working substance. 

It is convenient to approach the theory of heat-engines by 
considering, in the first instance, the action of an engine 
in which the working substance is any one of the so-called 
permanent gases, or a mixture of them, such as air. The word 
permanent, as applied to a gas, is to be understood only as meaning 
that the gas is liquefied with diflBculty — by the use of either ex- 
tremely low temperature or extremely high pressure or both to- 
gether. So long as gases are under conditions of pressure and tem- 
perature widely different from those which produce liquefaction, 
they conform very approximately to certain simple laws — laws 
which may be regarded as rigorously applicable to ideal sub- 
stances called perfect gases. Afber stating these laws we shall 
examine the efficiency of a heat-engine using a gas in a certain 
manner as working substance, and then show that the results 
so derived have a general application to all heat-engines whatsoever. 
In this procedure there is no sacrifice of generality, and a part of 
the i»x)cess is of independent service in the discussion of actual 


29. Laws of the permanent gases. Boyle's law. The 

laws of the permanent gases are the following: — 

Law 1 (Boyle). The volume of a given mass of gas varies 
inversely as the pressure, provided the temperature be kept constant. 

Thus, if V be the volume of a given quantity of any gas, and 
P the pressure, then so long as the temperature is unchanged — 

V varies inversely as P, or PF= constant. 

For air the value of this constant is 26220 when the temperature 
is 32** F., V being taken as the volume in cubic feet of 1 lb. of air, 
and P being expressed in pounds per square foot 

30. Charles's law. Law 2 (Charles). Under constant pres- 
sure equal volwmes of different gases increase equally for the same 
increment of temperature. Also, if a gas be heated under constant 
pressure, eqtml increments of its volume correspond very nearly to 
eqiud intervals of temperature as determined by the scale of a mer- 
cury thermometer. 

If, for example, we take a vessel containing a quantity of 
air and heat it from one temperature to another, taking care to 
arrange the experiment so that the air may expand without any 
change in its pressure, we shall find that a certain change of 
volume takes place. Let any other permanent gas then be substi- 
tuted for the air in the vessel and let the experiment be repeated 
by heating xthis other gas from the same initial to the same 
final temperature as before, the pressure being still kept constant. 
The volume will be found to have changed by sensibly the same 
amount as was observed in the experiment with air. And further, 
if the experiment be varied by using a greater or smaller interval 
of temperature, it will be found that the change of volume under- 
gone by the air or by any other gas that may be substituted for it 
is very approximately proportional to the magnitude of the 
interval of temperature as measured on the scale of the 
ordinary mercury thermometer. This is equivalent to saying that 
if we use an air-thermometer (where the air is allowed to 
expand without change of pressure) to measure temperatures, 
defining equal intervals of temperature to be those which corre- 
spond to equal expansions on the part of the air, we obtain 
a thermometric scale which is in substantial though not perfect 
agreement with the usual mercurial scale, which defines equal 


intervals of temperature to be those that ooirespond to equal 
expansions of mercury in glass. 

Experiment shows that the amount by which a gas expands 
when its temperature is changed by one d^pree Fahrenheit, the 
pressure being kept constant, is about ^ of its volume at 32"" F. 
Thus if we take 493 cubic inches of air or any other permanent gas 
at the temperature 32° and heat it to 33° its volume alters to 494 
cubic inches. If we heat it to 34° its volume becomes 495 cubic 
inches and so on. Similarly if the gas be cooled from 32° F. to 
31° F. its volume changes firom the original 493 cubic inches to 
492, and so on. 

Putting this in a tabular form, let the volume be 
493 at 32° F. 

It will become 492 at 31° F. 

461 at b°F. 

and finally would be 6 at - 461° F. 

if the same law could be held to apply at indefinitely low tempe- 
ratures. Any actual gas would change its physical state long 
before so low a temperature were reached. 

31. Absolute temperature. The above result may be con- 
cisely expressed by saying that if temperature be reckoned, not 
from the ordinary zero but from a point 461° below the zero of Fah- 
renheit's scale, the volume of a given quantity of a gas, kept at con- 
stant pressure, is proportional to the temperature reckoned from that 
zero. Temperatures so reckoned are called absolute temperatures, 
and the point — 461° F. is called the absolute zero of temperature. 
Denoting any temperature according to the ordinary scale by t, 
and the corresponding absolute temperature by t, we have 

T = ^ -h 461 on the Fahrenheit scale, 

and T = < -h 274 on the Centigrade scale. 

Charles's law shows that if temperatures be measured by ther- 
mometers in which the expanding substance is air, hydrogen, oxygen, 
or any other permanent gas, those intervals of temperature being 
called equal which correspond to equal amounts of expansion, then 
the indications of these thermometers always agree very closely 
with each other, and also agree, though less closely, with the 
indications of a mercury thermometer. It will be shown later that 


the theory of heat-engines affords a means of forming a truly 
absolute thermometric scale, in the sense that it is a scale which is 
independent of the properties, as to expansion, of any substance. 
We are therefore justified in the use of the term absolute, as 
applied to temperatures measured by the expansion of a gas. 

It will be further seen that this scale has the same absolute 
zero as we have arrived at here by considering the properties of 
the permanent gases, and also makes those intervals equal which 
are reckoned to be equal on the scale of the gas thermometer. 

32. Connection between Pressure, Volume, and Tem- 
perature in a gas. By Boyle's law we have P oc-p. where the 

temperature is kept constant, V being the volume of a given 
quantity of any gas. By Charles's law we have P oc t when V is 
kept constant, r being the absolute temperature. Combining the 
two laws, we have, for a given mass of any gas, 

PF=CT, (1) 

where c is a constant depending on the specific density of the gas 
and on the units in which P and V are measured. In what 
follows it will be assumed that P is measured in pounds per square 
foot, that V is the volume of 1 lb. in cubic feet, and that r is the 
absolute temperature expressed in Fahrenheit degrees. For air, 
with these units, 

PF «53-18t. 

33. The speoifio heat of a gas. Law 3 (Begnault). The 
specific heat at constant pressure is constant for any gas. 

By specific heat at constant pressure is meant the heat taken 
in by 1 lb. of a substance when its temperature rises V F., while 
the pressure remains unchanged — the volume being allowed to 
change. The law states that this quantity is the same for any 
one gas, no matter what be the temperature, or what the constant 
pressure, at which the process of heating takes place. 

Another important quantity in the theory of heat-engines 
is the specific heat at constant volume, that is, the heat taken in 
by 1 lb. of the substance when its temperature rises V F. while 
the volume remains unchanged — the pressure being free to change. 
We shall denote specific heat at constant pressure by Kp and 
specific heat at constant volume by JSTc. An obvious difference 



between the heating of a gas at constant pressure and at constant 
volume is that when heated at constant volume the gas does no 
work, whereas heating at constant pressure involves expansion of 
the gas and consequently the doing of an amount of work equal to 
the product of the pressure and the increase of volume. Let 1 lb. 
of a gas be heated at constant pressure P &om temperature Ti to 
temperature r, (absolute). Let Vi be the volume at Ti and F, the 
volume at r,. Heat is taken in, and external work is done by the 
expansion of the gas, namely — 

Heat taken in = ^|,(t, — Tj). 

Work done =P(F,- V^) = c(t, -tO- 

The difference between these quantities, or (^j, — c) (t, — Ti), is 
the amount by which the stock of internal energy possessed by 
the gas has increased during the process. It will be shown 
immediately that this gain of internal energy is the same 
when the gas has its temperature changed in any other manner 
from Ti to T) and is independent of the condition of the gas as 
to pressure. 

34. The Internal energy of a gas. Law 4 (Joule). When 
a gas expands without doing external work, and withotU taking in 
or giving out heat {and therefore vnihout changing its stock of 
internal energy)y its temperature does not change. 

This fact was established by the experiments of Joule. 
He connected a vessel containing compressed gas with another 
vessel which was empty, by means of a pipe with a closed stop-cock. 
Both vessels were immersed in a tub of water and were allowed to 
assume a uniform temperature. Then the stop-cock was opened, 
and the gas distributed itself between the two vessels, expand- 
ing without doing external work. After this the tempera- 
ture of the water in the tub was found to have undergone 
no change. The temperature of the gas was unaltered, and 
no heat had been taken in or given out by it, and no work had 
been done by it. 

Since the gas had neither gained nor lost heat, and had done 
no work, its internal energy was the same at the end as at the 
beginning of the experiment. The pressure and volume had 
changed, but the temperature had not. The conclusion follows 
that the internal energy of a given quantity of a gas depends only 


on its temperature, and not upon its pressure or volume; in other 
words, a change of pressure and volume not associated with a 
change of temperature does not alter the internal energy. Hence 
in any change of temperature the change of internal energy is 
independent of the relation of pressure to volume during the 
operation : it depends only on the amount by which the tempera- 
ture has been changed. 

To express the quantity of energy which becomes stored up 
in a gas when its temperature rises, or is extracted from the 
gas when its temperature falls, we may consider either the case 
of heating at constant volume, or at constant pressure, since 
the internal energy depends on the temperature and on nothing 

In the operation of heating any substance we have 
Heat taken in = work done + increase of internal energy. 

Take the case of heating at constant volume, and suppose a 
lb. of gas to be so heated from absolute temperature Ti to absolute 
temperature Tj. The heat taken in is 

by definition of K^, the specific heat at constant volume. No 
external work is done, and hence the whole of this heat goes to 
increase the stock of internal energy. But in whatever way the 
temperature be changed from Ti to Xg the change of internal 
energy is the same. Hence this expression 

measures the change of internal energy which 1 lb. of gas suflfers 
whenever its temperature changes from Ti to Tg in any manner 
whatsoever, no matter how the volume and the pressure vary 
during the process. 

35. Relation between the two Specific Heats. We are 

now in a position to establish a relation between the two specific 
heats of a gas, K^ and Kp, It was seen by § 33 that when a gas is 
heated from r^ to Tj in one particular way, namely, at constant 
pressure, the change of its internal energy per lb. may be 
expressed as 


This expression must agree with the one just found, and 

K,^K^-o, (2). 



The ratio -j^ enters into many thermodynamic equations 

and is usually denoted by the letter 7. Using this symbol the 
above equation may be written 

^• = 7^ (3)- 

36. Values of the constants for Air. The constant 26220 
given in § 29 as the value of PF when V is the volume in cubic 
feet of 1 lb. of dry air at 32"" F., and P is the pressure in pounds 
per square foot, is derived from a measurement of the density of 
air by Begnault. Taking the absolute zero of temperature to be 
461 degrees below the zero of Fahrenheit's scale, we divide this 
number by 493 to find c in the formula PV^cr. This makes 

Begnault's measurements of the specific heat of dry air give 
0-2375 thermal units as the value of Kp, Taking r to be 778, 
this is equivalent to 184*8 foot-pounds. Subtracting c fix>m this 
we find Kt, to be 131'6 foot-pounds, or 0'1691 thermal units. With 
these data the ratio of the specific heats, Kp/Kt, or 7, is therefore 
1*404. Determinations of 7 in air by other methods have generally 
given a slightly higher value, such as 1*408. For most calculations 
1*4 is near enough. 

To find the constants for other gases, take values of c inversely 
proportional to the density as given in Regnault's Tables^ These 
tables also give values of Kp, K^ is then found by subtraction of c 
from Kp, 

37. Work done by an expanding fluid. We now 

return to the consideration of imaginary indicator diagrams, 
which exhibit the relation of the pressure to the volume of a 
fluid working substance during its expansion or during its 
compression, in order to study the form which the expansion or 
compression curve assumes in certain particular cases. 

In most of the instances which present themselves in the 
theory of heat-engines such curves may be exactly or approxi- 
mately represented by an equation of the form 

PF'« = constant, 

1 See Eyerett's VmU and Physical Constants. 



where the index n has various numerical values but is a constant 
for any one curve. We proceed to find 
the values which n takes in two very im- 
portant modes of expansion. Let AB, 
figure 10, be a curve of expansion, for any 
fluid, to which the general formula PV^ = 
constant is applicable. The fluid is sup- 
posed to expand from A, where the pressure 
is Pi and the volume Fj, to B, where the 
pressure is Pj and the volume is Fj. 
During this expansion it does an amount of work which is 
measured by the shaded area under the curve. That is to say, 
if W denote the work done during expansion. 

Pig. 10. 

Jvt - 




the integral being taken between the limits F, and Fj. To 
integrate we have to remember that the pressure and volume 
at any point are such that 

Hence substituting 
work done becomes 


for, P in (4), this expression for the 

which gives on integration 

y_ PtF,'>(F,'-"-F.'^) 



This may also be written 




where r is the ratio of expansion, that is to say, the ratio of the 
final volume F, to the initial volume Fi. 

Since PiFi* = PjF,**, still another form in which the above 
result may be expressed is readily derived firom equation (5), 

n-1 ^'^' 



If instead of expanding from A U> B the fluid were compressed 
from B to A the expresaon given above for W will measure the 
work spent upon the fluid instead of work done by it. 

Further, if the working substance be a gas, in which (by the 
laws of Boyle and Charles) P F= cr, equation (7) may be written 

^=^fe^ (8). 

since PiFi = cti and Pa'^a= CTf 

38. Adiabatic Expaniion. We have next to consider 
particular modes in which any working substance may be ex- 
panded or compressed. One very important case is that which 
occurs when the fluid neither receives nor rejects heat as it 
expands, or as it is compressed. This mode of expansion or 
compression is called adiaAatic, and a curve which exhibits 
the relation 5f P to F in such a process is called an adia- 
batic line. In any adiabatic process the substance is neither 
gaining nor losing heat by conduction or radiation or internal 
chemical action. Hence the work which a substance does when it 
is expanding adiabatically is all done at the expense of its stock 
of internal energy, and the work which is spent upon a substance 
when it is being compressed adiabatically all goes to increase its 
stock of internal energy. Adiabatic action would be realized if we 
had a substance expanding, or being compressed, without chemical 
change, in a cylinder which (along with the piston) was a perfect 
non-conductor of heat, and was opaque to heat-rays. 

In actual heat-engines the action is never strictly adiabatic 6n 
account of the fact that more or less heat passes by conduction 
between the working fluid and the inner surface of the cylinder. 
The more quickly the process of expansion or compression is 
performed the more nearly adiabatic it becomes, for there is then 
less time for this transfer of heat to take place. 

Coming now to the particular case in which the working 
substance is a gas, since in adiabatic expansion or compression 
the work done is equal to the change of internal energy we may 
determine the law of adiabatic action in a gas as follows. Taking 
expression (8) for the work done, namely, 

^^ c(Ti-Ta) 

w — 1 

elemeKtary theory of heat-engines, 47 

we have to find what value of n in the general formula PV^=^ 
constant will make the process adiabatia We have seen (§ 34) 
that in any change of temperature from Ti to Tj a gas loses internal 
energy to the amount 


which may be written 

7 being (§ 35) the ratio of the two specific heats. 

Hence, equating the work done with the loss of internal energy, 
the condition of adiabatic expansion is secured when 

(ti - T a) _ o(Ti-Ta) . . 

"ir=a" " 7-1 • ^^^' 

from which w = 7. 

Expansion or compression will therefore be adiabatic when 

PFy = constant, (10), 

or in other words this is the equation of an adiabatic line for a gas. 

39. Change of temperature in the adiabatic expansion 
of a gas. When a gas is expanding adiabatically its stock of 
internal energy is being reduced, and hence its temperature 
(to which the internal energy is proportional, by § 34) falls. Con- 
versely, in adiabatic compression the temperature rises. The 
amount by which the temperature changes is found by com-' 
bining the equations 

Multiplying them together we have 

T._ P,nPiF,y 

whence Trirr 

where r is as before the ratio of expansion. This result of course 
applies to compression as well as to expansion along an adiabatic 



48 elehentart theory of heat-engines. 

As to expansions which are not adiabatic, it follows, from the 
expressions given above for the external work done by an 
expanding gas and for the change of internal energy, that if n 
is less than 7 the work done is greater than the loss of internal 
energy — ^that is to say, the gas is then taking in heat while it 
expands. On the other hand if n is greater than 7 the work done 
is less than the loss of internal energy ; in other words, the gas is 
then rejecting heat by conduction to the walls of the containing 
vessel or in some other way. 

By way of exemplifying an adiabatic process suppose a quan- 
tity of dry air to be contained in a cylinder at a temperature of 
60° Fah. (t = 521) and to be suddenly compressed to half its original 
volume, the process being so rapid that no appreciable part of 
the heat developed by compression has time to pass from the air 
to the cylinder walls. Here r = J, and taking 7 for air to be 1*404 
the temperature immediately after compression, before the gas has 
time to cool is 

T, = T, (^Y" = 521 X 2^ = 689 

or 228*^ Fah. The work spent in compressing the air, namely, 
c(t,-Ti). 5318x168 ««,,^- . , 

^ ' ^ IS jr-rzrz = 22110 foOt-pOUuds, 

7 — 1 0'404 " 

for each lb. of air in the cylinder. The internal energy of the 
gas becomes increased by this amount; but if the cylinder 
be a conductor of heat the whole of this will in time become 
dissipated by conduction to surrounding bodies and the internal 
energy will gradually return to its original value, as the tempera- 
ture of the gas sinks to 60° Fah. 

During compression the pressure rises (following the law 
P7V = constant) and just at the end its value is greater than at 
the beginning in the ratio r^ to 1, that is 2^-^ or 2*65 to 1. If 
as before we suppose the temperature to sink slowly by conduction 
to 60° Fah. while the volume does not change, the pressure will 
fall with the temperature until it reaches a value only twice that 
which it had before the air was compressed, 

40. Iiothermal Expansion. Another very important mode 
of expansion or compression is that called isothermal, in which the 
temperature of the working substance is kept constant during the 


In the case of a gas the curve of isothermal expansion is a 
rectangular hyperbola, having the equation 

PF= constant = CT (12). 

This is a particular case of the general formula PV^ = constant. 
But equation (6) or (7) above will not serve to find the work done, 
for when n = 1 both the numerator and the denominator in these 
expressions vanish. To find the work done in the isothermal ex- 
pansion of a gas we have 


and ^ = ^' 

from which Tr= PJT^ J ' ~r ' 

Integrating, W = P.V, (log. F, - log. V,) 
or Tr = P,F,log.^=P,F,log.r (13). 

Instead of PiFi we may write PV, since the product of P 
and Fis constant through the process, and again, since PF = ct, 

F=CTlog.r (14). 

There is no need here to use a sufl&x with t since the tempera- 
ture does not change. These expressions give either the work 
done by a gas during isothermal expansion or the work spent upon 
it during isothermal compression \ 

During isothermal expansion or compression a gas suflfers no 
change of internal energy (by § 34, since t is constant). Hence 
during isothermal expansion the gas must 
take in an amount of heat just equal to 
the work it does, and during isothermal 
compression it must reject an amount 
of heat just equal to the work spent 
upon it. The expression crlog.r con- 
sequently measures, not only the work 
done by or upon the gas, but also the 
heat taken in during isothermal expan- ^«« vi- 

sion or given out during isothermal 

^ In calculations where this expression is involved it is convenient to remember 
that log,, the 'hyperbolic/ or 'natural/ or 'Napierian' logarithm, of any number 
is 2*3026 times the common logarithm of the number. 

E. 4 




compression. In the diagram, fig. 11, the line AB is an example 
of a curve of isothermal expansion for a perfect gas, called for 
brevity an isothermsd line, while AC ia An adiabatic line starting 
from the same point A. 

The compression of air or any other gas in a real cylinder is 
approximately adiabatic when the process is very quickly per- 
formed, but approximately isothermal when it is performed so 
slowly that the heat has time to be dissipated by conduction while 
the process goes on. 

41. Camot's Cycle of operations. We shall now consider 
the action of an ideal engine in which the working substance is a 
perfect gas, that is caused to pass through a cycle of changes each 

Fig. 12. — Camot's Cyole, with a gas for working substance. 

of which is either isothermal or adiabatic. The cycle to be 
described was first examined by Carnot, and is spoken of as 
Camot's cycle of operations. Imagine a cylinder and piston 
composed of a perfectly non-conducting material, except as regards 
the bottom of the cylinder, which is a conductor. Imagine also a 
hot body or indefinitely capacious source of heat A, kept always at 
a temperature Ti, also a perfectly non-conducting cover B, and a 
cold body or indefinitely capacious receiver of heat G, kept always 


at some temperature r, which is lower than Ti. It is supposed 
that A, B, or G can be applied at will to the bottom of the 
cylinder. Let the cylinder contain 1 lb. of a perfect gas, at 
temperature Tj, volume F», and pressure Pa to begin with. The 
suffixes refer to the points on the indicator diagram, fig. 12. 

(1) Apply Ay and allow the piston to rise slowly through any 
convenient distance. The gas expands isothermally at Ti, taking 
in heat from the hot source A and doing work. The pressure 
changes to P^ and the volume to Fj. 

(2) Remove A and apply B. Allow the piston to go on 
rising. The gas expands adiabatically, doing work at the expense 
of its internal energy, and the temperature falls. Let this go on 
until the temperature is Tj. The pressure is then P<„ and the 
volume Fc. 

(3) Remove B and apply G. Force the piston down slowly. 
The gas is compressed isothermally at Tj, since the smallest 
increase of temperature above Ta causes heat to pass into G. 
Work is spent upon the gas, and heat is rejected to the cold 
receiver G. Let this be continued until a certain point d (fig. 12) 

is reached, such that the fourth operation will complete the cycle, l ^ 

(4) Remove G and apply B. Continue the compression, 
which is now adiabatic. The pressure and temperature rise, and 
if the point d has been properly chosen, when the pressure is 
restored to its original value P^, the temperature will also have 
risen to its original value Tj. [In other words, the third operation 
must be stopped when a point d is reached such that an adiabatic 
line drawn through d will pass through a.] This completes the cycle. 

To find the proper place at which to stop the third operation, 
we have by equation (11), for the cooling during the adiabatic 
expansion of stage (2), 

Ta \Vj 

and also, for the heating during the adiabatic compression of 
stage (4), 

Ta \Vj • 
Hence W'^W^ 

yh y a 

and therefore also 



That is to say, the ratio of isothermal compression in the third 
stage of the cycle is to be made equal to the ratio of isothermal 
expansion in the first stage, in order that an adiabatic line through 
d shall complete the cycle. For brevity we shall denote either of 
these last ratios (of isothermal expansion and compression) by r. 

The following are the transfers of heat to and from the 
working gas, in the four successive stages of the cycle: — 

(1) Heat taken in from -4 = cti log, r (by § 40). 

(2) No heat taken in or rejected. 

(3) Heat rejected to (7 = cr, log. r (by § 40). 

(4) No heat taken in or rejected. 

Hence, the net amount of external work done by the gas, 
being the excess of the heat taken in above the heat rejected in 
a complete cycle, is 


this is the area enclosed by the four curves in Fig. 12. 

42. Efficiency in Camot's Cycle. The efficiency of the 
engine, namely, the fraction 

Heat converted into work 
Heat taken in 

is c(T,-T,)log.r^T^-^, 

This is the fraction of the whole heat given to it which ,an 
engine following Camot's cycle converts into work. The engine 
takes in an amount of heat, at the temperature of the source, 
proportional to r^\ it rejects an amount of heat, at the temperature 
of the receiver, proportional to Tj. It works within a range of 
temperature extending from Ti to Tj, by letting down heat from Ti 
to Ta (§ 25), and in the process it converts into work a fraction of 
that heat, which fraction will be greater the lower the tempera- 
ture Ta at which heat is rejected is below the temperature r^ at 
which heat is received. 

43. Camot'8 cycle reversed. Next consider what will 
happen if we reverse Camot's cycle, that is to say, if we force 
this engine to act so that the same indicator diagram as before is 
traced out, but in the direction opposite to that followed in § 41. 


Starting as before from the point a (fig. 12) and with the gas 
at Ti, we shall require the following four operations : — 

(1) Apply B and allow the piston to rise. The gas expands 
adiabatically, the curve traced is od, and when d is reached the 
temperature has fallen to Tj. 

(2) Remove B and apply C. Allow the piston to go on 
rising. The gas expands isothermally at Ts, tcJcing heat from 0, 
and the curve do is traced. 

(3) Remove G and apply B. Compress the gas. The process 
is adiabatic. The curve traced is c6, and when 6 is reached the 
temperature has risen to Ti. 

(4) Remove B and apply A. Continue the compression, 
which is now isothermal, at r^. Heat is now rejected to A, and 
the cycle is completed by the curve 6a. 

In this process the engine is not doing work ; on the contrary, 
a quantity of work is spent upon it equal to the area of the 
diagram, or c(ti --T2)loger, and this work is converted into heat. 
Heat is taken in from G in the first operation, to the amount 
CTalog.r. Heat is rejected to A in the fourth operation, to the 
amount CTilog.r. In the first and third operations there is no 
transfer of heat. 

The action is now in every respect the reverse of what it was 
before. The same work is now spent upon the engine as was 
formerly done by it. The same amount of heat is now given to 
the hot body A as was formerly taken from it. The same amount 
of heat is now taken from the cold body G as was formerly given 
to it, as will be seen by the following scheme : — 

Gamofs Gycle, Direct, 

Work done by the gas = c (ti — Tj) log, r ; 
Heat taken from A = cti log, r ; 
Heat rejected to G=ct^ log.r. 

Gamot's Gycle, Reversed, 
Work spent upon the gas = c (ti — Tj) log, r ; 
Heat rejected to -4 = cti log, r ; 
Heat taken from (7 = era log, r. 

The reversal of the work has been accompanied by an exact 
reversal of each of the transfers of heat. 


44 Rerenible engine. An engine in which this is possible 
is called, from the thermodynamic point of view, a retfersible 
engine. In other words, a reversible heat-engine is one which, if 
forced to trace out its indicator diagram reversed in direction, so 
that the work which would be done by the engine, when running 
direct, is actually spent upon it, will reject to the source of heat 
the same quantity of heat as, when running direct, it would take 
from the source, and will take from the receiver of heat the same 
quantity as, when running direct, it would reject to the receiver. 
By " the source of heat *" is meant the hot body which acts as 
source when the engine is running direct, and by " the receiver " 
is meant the cold body which then acts as receiver. An engine 
performing Camot's cycle of operations is one example of a re- 
versible engine. The idea of thermodjniamic reversibility in the 
sense here defined is of the greatest interest, for the reason that 
no heat-engine can be more efficient than a reversible engine 
when both work between the same limits of temperature ; that is 
to say, when both engines take in heat at the same tempera- 
ture and also reject heat at the same temperature. This theorem, 
due to Camot, is of fundamental importance in the theoiy of heat- 
engines. It is deduced as follows from the laws of thermo- 

46. Oamot'8 Principle. To prove that no other heat- 
engine can be more efficient than a reversible engine when both 
work between the same limits of temperature, imagine two 
engines R and 8 of which R is reversible, and let them work by 
taking in heat from a hot body A and by rejecting heat to a cold 
body G. Let Q^ be the quantity of heat which the reversible 
engine R takes in from A for each unit of work which it does 
and let Qc be the quantity which it rejects to C, 

Now consider what consequences would follow if it were 
possible for fif to be more efficient than R. It would take in less 
heat frt)m A and reject correspondingly less heat to C, in doing 
each unit of work. Denote the heat which it would take in from 
-4 by Qui — ? M^d the heat which it would reject to C by Qo— ?• 

Suppose that 8 working direct (that is to say, converting heat 
into work) be set to drive i2 as a reversed engine, so that R 
converts work into heat For every unit of work done by the 
engine 8 on the reversible engine R the quantity Q^ — ? would 


be taken from A by the engine 8, and the quantity Q^ would 
be restored to A by the reversed action of the engine R. This 
is because R being reversible restores to A when working reversed 
the same amount of heat as it would take from A when working 
direct. Hence the hot body would on the whole gain heat, by the 
amount q for every unit of work done by the one engine on the 
other. Again, S gives to C7 a quantity Qc — q while -B takes from 
C a quantity Qc and hence the cold body C would lose an amount 
of heat equal to q for every unit of work done by the one engine 
or the other. Thus the combined action of the two engines — one 
working direct, as a true heat-engine and the other reversed, as 
what we might call a heat-pump, would result in a transfer of 
heat from the cold body C to the hot body A, and this process 
might evidently go on without limit. Moreover the two engines 
taken together form a purely self-acting system, for the whole 
power generated in one is spent on the other and is sufficient to 
drive the other ; if we assume that there is no mechanical friction 
the double machine requires no help from without. Hence the 
supposition that the engine /S could be more efficient than the 
reversible engine R has led to a result inconsistent with the 
second law of thermodynamics for it has led us to construct, in 
imagination, a self-acting machine capable of transferring heat, in 
any quantity, from a cold body to- a hot body. The second law 
asserts that this is contrary to all experience, and we are there- 
fore forced to the conclusion that no other engine S can be more 
efficient than a reversible engine R when both work between the 
same limits of temperature. In other words, when the source 
and receiver of heat are given a reversible heat-engine is as 
efficient as any engine working between them can be. 

Further, let both engines be reversible. Then the same 
argument shows that neither can be more efficient than the other. 
Hence all reversible heat-engines taking in and rejecting heat at 
the same two temperatures are equally efficient. 

46. Revenibility the criterion of perfection in a heat- 
engine. These results imply that reversibility, in the thermo- 
dynamic sense, is the criterion of what may be called perfection in 
a heat-engine. A reversible engine is perfect in the sense that it 
cannot be improved on as regards efficiency: no other engine, 
taking in and rejecting heat at the same temperatures, will 


convert into work a greater fraction of the heat which it takes in. 
Moreover, if this criterion be satisfied, it is as regards efficiency a 
matter of complete indifference what is the nature of the working 
substance, or what, in other respects, is the mode of the engine's 

47. Efficiency of a perfect heat-engine. Further, since 
all engines that are reversible are equally efficient, provided they 
work between the same temperatures, an expression for the 
efficiency of one will apply equally to all. Now, the engine whose 
efficiency was found in § 42, namely, an engine having a gas for 
working substance and performing Camot's Cycle of operations, 
is one example of a reversible engine. Hence the expression 
which was obt«dned for its efficiency, namely, 

is the efficiency of any reversible heat-engine whatsoever taking 
in heat at Tj and rejecting heat at Tj. And, as no engine can be 
more efficient than one that is reversible, this expression is the 
measure of perfect efficiency. We have thus arrived at the 
immensely important conclusion that no heat-engine can convert 
into work a greater fraction of the heat which it receives thaa is 
expressed by the excess of the temperature of reception above that 
of rejection divided by the absolute temperature of reception. 

48. Summary of the argument Briefly recapitulated, the 
steps of the argument by which this result has been reached are 
as follows. After stating the experimental laws to which gases 
conform and finding that they afforded a provisional means of 
defining temperature upon an absolute scale we examined the 
action of a heat-engine in which the working substance took in 
heat when at the temperature of the source and rejected heat 
when at the temperature of the receiver, the change of tempera- 
ture from one to the other of these limits being accomplished by 
adiabatic expansion and adiabatic compression. Taking a special 
case in which the engine had for its working substance a perfect 
gas, we found that its efficiency was (ti — T2)/ti (§ 42). We also 
observed that it was, in the thermodynamic sense, a reversible 
engine (§ 44). Then we found, by an application of the second 
law of thermodjmiamics, that no heat-engine can have a higher 


eflSciency than a reversible engine, when taking in and giving out 
heat at the same two temperatures Ti and Tj ; this was shown by 
the fact that a contrary assumption would lead to a violation of 
the second law (§ 45). Hence, we concluded that all reversible 
heat-engines receiving and rejecting heat at the same tempera- 
tures, Ti and Ta respectively, are equally efficient, and hence that 
the efficiency 

already determined for one particular reversible engine, is the 
efficiency of any reversible engine, and is a limit of efficiency 
which no engine whatever can exceed. 

Another way of stating the performance of a perfect engine 
evidently is to say that the heat taken in is to the heat rejected as 

Ti is to Tj. 

49. Conditions of maximum efficiency. The availability 
of heat for transformation into work depends essentially on the 
range of temperature through which the heat is let down from 
that of the hot source to that of the cold body into which heat is 
rejected; it is only in virtue of a diflference of temperature 
between bodies that conversion of any part of their heat into 
work becomes possible. No mechanical effect could be produced 
from heat, however great the amount of heat obtainable, if all 
bodies were at a dead level of temperature. Again, it is im- 
possible to "Convert the whole of any supply of heat into work 
because it is impossible to reach the absolute zero of temperature 
at the lower end of the temperature range. 

If Ti and Ta are given as the highest and lowest temperatures 
of the range through which a heat-engine is to work, it is clear 
that the maximum of efficiency can be reached only when the 
engine takes in all its heat at Ti and rejects at r, all that is 
rejected. With respect to every portion of heat taken in and 
rejected the greatest ideal efficiency is 

Temperature of reception — temperature of rejection 
Temperature of reception 

Any heat taken in at a temperature below ti or rejected at a 
temperature above r^ will have less availability for conversion into 
work than if it had been taken in at Ti and rejected at Tg, and 


hence, with a given pair of limiting temperatures, it is essential to 
maximum e£Sciency that no heat be taken in by the engine except 
at the top of the range, and no heat rejected except at the bottom 
of the range. Further, as we have seen in § 45, when the tempe- 
ratures at which heat is received and rejected are assigned, an 
engine attains the maximum of efficiency if it be reversible. 

60. Conditions of revenibllity. It is therefore important 
to inquire more particularly what kinds of action are reversible in 
the thermodjmamic sense. A little consideration will show that a 
transfer of heat from the source or to the receiver is reversible 
only when the working substance is at sensibly the same tempera- 
ture as the source or the receiver, as the case may be, and an 
expansion is reversible only when it occurs by the gradual dis- 
placement of some part of the containing envelope in such a 
manner that the expanding fluid does external work on the 
envelope, and does not waste energy to any sensible extent in 
setting itself in motion* This excludes what may be termed free 
expansion, such as that of the gas in Joule's experiment, § 34, and 
it excludes also what may be called imperfectly-resisted expansion, 
such as would occur if the fluid were allowed to expand into a 
closed chamber in which the pressure was less than that of the 
fluid, or if the piston in a cylinder rose so fast as to cause, through 
the inertia of the expanding fluid, local variations of pressure 
throughout the cylinder. A similar condition of course applies in 
regard to the compression of the working fluid : neither expansion 
nor compression must take place in such a manner as to set up 
eddies within the fluid. 

To make a heat-engine, working within given limits of tempe- 
rature, as efficient as possible the conditions to aim at therefore 
are — (1) to take in no heat except at the highest temperature, 
and to reject no heat except at the lowest temperature, (2) to 
secure that the working substance shall, when receiving heat, be 
at the temperature of the body from which the heat comes, and 
that it shall, when giving up heat, be at the temperature of the 
body to which heat is given up ; (3) to avoid free or imperfectly- 
resisted expansion. If these conditions are fulfilled the engine is 
a reversible heat-engine and the most efficient possible within the 
given range of temperatures. 

The first and second of these conditions are satisfied if in the 


action of the engine the working substance changes its tempera- 
ture from Ti to Tj by adiabatic expansion, and from Tj to Tj by 
adiabatic compression, thereby being enabled to take in and reject 
heat at the ends of the range without taking in or rejecting any 
by the way. This is the action in Camot's ideal engine (§ 41). 

61. Perfect Engine using Regenerator. But there is 
another way in which the action of a heat-engine may be made 
reversible. Suppose that the working substance can be caused to 
deposit heat in some body within the engine while passing from 
Ti to T3, in such a manner that the transfer of heat from the 
substance to this body is reversible (satisfying the second con- 
dition above), then when we wish the working substance to pass 
from Ta to Ti we may reverse this transfer and so recover the 
heat that was deposited in this body. This alternate storing and 
restoring of heat would serve, instead of adiabatic expansion and 
compression, to make the temperature of the working substance 
pass from Ti to Tj and from Tj to Ti respectively. The alternate 
storing and restoring is an action occurring wholly within the 
engine, and is therefore distinct from the taking in and rejecting 
of heat by the engine. 

In 1827 Bobert Stirling designed an apparatus, called a re- 
generator y by which this process of alternate storing and restoring 
of heat could be actually performed. For the present purpose it 
will suffice to describe the regenerator as a passage through which 
the working fluid can travel in either direction, whose walls have 
a very large capacity for heat, so that the amount alternately 
given to or taken from them by the working fluid causes no more 
than an insensible rise or &11 in their temperature. The tempe- 
rature of the walls at one end of the passage is Tj, and this falls 
continuously down to Tj at the other end. When the working 
fluid at temperature Ti enters the hot end and passes through, it 
comes out at the cold end at temperature T3, having stored in the 
walls of the regenerator a quantity of heat which it will pick up 
again when passing through in the opposite direction. During the 
return journey of the working fluid through the regenerator from 
the cold to the hot end its temperature rises from Tj to Ti by 
picking up the heat which was deposited when the working fluid 
passed through from the hot end to the cold. The process is 
strictly reversible, or rather would be so if the regenerator had an 



unlimited capacity for heat, if no conduction of heat took place 
along its waUs from the hot to the cold end, and if no loss took 
place by conduction or radiation from its external sur&ce. 

62. Stirling's BegeneratiTe Air-Engine. Using air as 
the working substance, and emplo3ring his regenerator, Stirling 
made an engine (to be described later) which, allowing for 
practical imperfections, is the earliest example of a truly rever- 
sible engine. The cycle of operations in Stirling's engine was 
substantially this: 

(1) Air (which had been heated to Ti by passing through the 
regenerator) was allowed to expand isothermally through a ratio r, 
taking in heat from a furnace and raising a piston. Heat taken 
in (per lb. of air) = cti log, r. 

(2) The air was caused to pass through the regenerator from 
the hot to the cold end, depositing heat and having its tempera- 
ture lowered to Ts, without change of volume. Heat stored in 
regenerator = K^, (ti — Ts). The pressure of course fell in propor- 
tion to the fall in temperature. 

(3) The air was then compressed isothermally to its original 
volume at Tj in contact with a refrigerator (or receiver of heat). 
Heat rejected = ctj log, r. 

(4) The air was again passed through the regenerator from 
the cold to the hot end, taking up heat 

and having its temperature raised to 
Ti. Heat restored by the regenerator 
= ir„(Ti — Ta). This completed the cycle. 
The eflSciency is 

CTi log, r-CTj log, r ^ Ti - Ta 

CTjl0g,r Ti 

The indicator diagram of this action 
is shown in fig. 13. Stirling's engine is 
important, not as a present-day heat- 
engine (though it has recently been re- 
vived in small forms after a long interval 

of disuse), but because it is typical of the ^lo. 13. IdwJ Mcator dia- 
^ •'* gram of Air-Engine with 

only mode, other than Camot's plan of Regenerator (Stirling). 

adiabatic expansion and compression, by 

which the action of a heat-engine can be made reversible. 



regenerative principle has been largely used in metallurgy and 
other industrial processes: the Siemens steel-fdmace is an 
example of its application on a large scale. Notwithstanding the 
immensely valuable services which the regenerator has rendered 
in such processes, its application to heat-engines has hitherto been 
very limited. Another way of using it in air-engines was tried 
by Ericsson, who kept the pressure instead of the volume constant 
while the working air was passed through the regenerator, thus 
getting an indicator diagram consisting of two isothermal lines 
and two lines of equal pressure. Attempts have also been made 
by Siemens and by Fleeming Jenkin to apply it to steam-engines 
and to gas-engines. 'But almost all actual engines, in so far as 
they can be said to approach the condition of reversibility, do so, 
not by the use of the regenerative principle, but by more or less 
nearly adiabatic expansion and compression after the manner of 
Camot's ideal engine. 



63. Formation of steam under constant pressure. We 

have now to consider the action of heat-engines in which the 
working substance is water and water-vapour or steam, and as a 
preliminary to this it is necessary to give some account of the 
physical properties of steam as determined by experiment. The 
properties of steam are most conveniently stated by referring in 
the first instance to what happens when steam is formed wnder 
constant pressure. This is substantially the process which occurs 
in the boiler of a steam-engine when the engine is at work. JTo 
fix the ideas we may suppose that the vessel in which steam is to 
be formed is a long upright cylinder fitted with a piston which 
may be loaded so that it exerts a constant pressure on the fluid 
below. Let there be, to begin with, at the foot of the cylinder a 
quantity of water (which for convenience of numerical statement 
we shall take as 1 lb.), at any temperature ^o ; ^^^^ let the piston 
press on the surface of the water with a force of P lbs. per square 
foot. Let heat now be applied to the bottom of the cylinder. As 
it enters the water it will produce the following effects in three 
stages : — 

(1) The temperature of the water rises until a certain tempe- 
rature t is reached, at which steam begins to be formed. The 
value of t depends on the particular pressure P which the piston 
exerts. Until the temperature t is reached there is nothing but 
water below the piston. 


(2) Steam is formed, more heat being taken in. The piston 
(which is supposed to exert a constant pressm^) rises. No further 
increase of temperature occurs during this stage, which continues 
until all the water is converted into steam. During this stage the 
steam which is formed is said to be saturated. The volume which 
the piston encloses at the end of this stage, — ^the volume, namely, 
of 1 lb. of saturated steam at pressure P (and temperature t\ — 
will be denoted by V in cubic feet. 

(8) If after all the water is converted into steam more heat 
be allowed to enter, the volume will increase and the temperature 
will rise. The steam is then said to be superheated. 

64. Saturated and superheated steam. The difference 
between saturated and superheated steam may be expressed by 
saying that if water (at the temperature of the steam) be mixed 
with steam some of the water will be evaporated if the steam is 
superheated, but none if the steam is saturated. Any vapour in 
contact with its liquid and in thermal equilibrium is necessarily 
saturated. When saturated its properties differ considerably, as a 
rule, from those of a perfect gas, but when superheated they 
approach those of a perfect gas more and more closely the farther 
the process of superheating is carried, that is to say, the more the 
temperature is raised above t, the temperature of saturation 
corresponding to the given pressure P. Saturated steam at a 
given pressure can have but one temperature ; superheated steam 
at the same pressure can have any temperature higher than that. 

65. Relation of pressure and temperature in saturated 
steam. The temperature t at which steam is formed depends on 
the value of P. Their relation was determined with great care 
by Regnault, in a series of classical experiments on which our 
knowledge of the properties of steam chiefly depends \ The 
pressure of saturated steam rises with the temperature at a rate 
which increases rapidly in the upper regions of the scale. This 
will be apparent from the first and second columns of Table I., 
given on p. 65, which is compiled from Rankine's reduction 
of Regnault's results. The first column gives the temperature on 

^ Mem. Iiut. Franee, 1847, vol. zxi. An aooonnt of Begnault's methods of 
experiment and a statement of his results expressed in British measures will be 
found in Dixon's Treatise on Heat, (Dublin, 1849). 


the Fahr. scale; the second gives the corresponding pressure in 

pounds per square inch. Rankine has also expressed the relation 

of temperature and pressure in saturated steam by the following 

formula (which is applicable with other constants to other 

vapours ^) : — 

1 ..lAA^T 2732 396945 ,,, 

logp = 6-1007-— ^ :^ (1), 

where p is the pressure in pounds per square inch, and r is the 
absolute temperature in Fahr. degrees. For most purposes, how- 
ever, it is more convenient to find the pressure corresponding to a 
given temperature, or the temperature corresponding to a given 
pressure, from the table either by interpolation or by drawing a 
portion of the curve connecting P with t A more extended table 
will be found in the Appendix, where the temperature of saturated 
steam, to the nearest half degree, is given for various pressures. 

66. Relation of pressure and volume in saturated steam. 

Table I. also shows the volume F, in cubic feet, occupied by 1 lb. 
of saturated steam at each pressure, and a more extensive series of 
values are given in the table in the Appendix. The volume of a 
pound of saturated steam at any assigned pressure is a quantity 
diflBcult to measure by direct experiment. It may, however, 
be calculated, from a knowledge of other properties of steam, 
by a process which will be described in the next chapter 
(§ 74). The values of V given in the table were determined by 
means of this process; they agree fairly well with such direct 
observations of the density of steam as have hitherto been made \ 
The relation of P to F may be approximately expressed by the 

PF^ = constant (2) 

1 Phil, Mag. Dec. 1864, or Manual of the SUam-Engine, p. 237. 

* The values of V given in the table are fonnd from those given by BanMne 
in his treatise on the Steam-Engine. He employed the method of calcnlating 7 
alluded to in the text, but the numbers whioh he gave require alteration in con- 
sequence of the fact that c7, the mechanical equivalent of heat, enters into the 
formula (see § 74) ; the calculated values of V are in fact nearly proportional to J, 
In Bankine's calculation J was taken as 772 : since the number 778 has been adopted 
here the values'* of V given in the table are increased nearly in the ratio of 
778 to 772. 

' This is Bankine*s formula. Zeuner considers that the curve of P and V for 
saturated steam is better expressed by using a slightly different index, and gives the 
equation PF^*<*^= constant. 

Table I. — Properties of SaJtwtcAed Steam. 6 

on Fahrenheit 



Heat of Formation. 

of lib. 





lb. per sq. in. 

Cub. Ft. 

Thermal Units. 

Thermal Units. 































































































































































281 -1 































, 374 




































the value of the constant (if / be taken as 778) being about 
69000 when P is stated in Iba per sq. foot and Fin cub. feet per lb. 
The student will find it useful to draw curves, with the data 
of the Table, showing the relation between the pressure and the 
temperature of saturated steam and also the relation of pressure to 

volume [or to the density, which is t^) , especially within the range 

usual in steam-engine practice. He will observe that -^ , the rate 

of change of pressure with respect to change of temperature in- 
creases rapidly as the temperature rises, and hence that in the 
upper part of the range a very small elevation of temperature in 
a boiler is necessarily associated with a large increment of pressure. 
The familiar case of water boiling in a kettle or other open vessel is 
only a special case of the formation of steam under constant pressure. 
There the constant pressure is that of the atmosphere, which is 14*7 
lbs. per square inch or thereabouts (as indicated by the barometer) 
and consequently the temperature at which the water boils is 
about 212° F. 

67. Supply of heat in the fbrmation of steam under con- 
stant pressure. We have next to consider the supply of heat in 
the imaginary experiment of § 53 in which 1 lb. of water initially at 
some temperature ^o is first heated to the boiling point and then con- 
verted into steam, under a constant pressure P, this constant pres- 
sure determining what the temperature of the boiling point shall 
be. During the first stage, while the temperature is rising from its 
initial value ^o to t, no steam is formed, and heat is required only 
to warm the water. Since the specific heat of water is nearly 
constant, the amount of heat taken in during the first stage 
is approximately t — to thermal units or J(t — to) foot-pounds, 
and this expression will generally serve with sufficient accuracy 
in practical calculations. More exactly, however, the heat taken 
in is in general somewhat greater than this, for Regnault's 
experiments show that the specific heat of water increases 
slightly at high temperatures. In stating the amount of heat 
required for this first stage, ^o must be taken as a known 
temperature; for convenience in numerical statement the tem- 
perature 32° F. is usually chosen as an arbitrary starting-point 
from which the reception of heat is to be reckoned. We shall 


employ the symbol h to designate the heat required to raise 1 lb. 
of water from 32° F. to the temperature t at which steam begins 
to form. The value of A in thermal units is given, approximately, 
by the formula 

h^t-Z2 (3). 

More exact values, which take account of the variation in the 
specific heat of water as determined experimentally by Regnault 
will be found in the last column of Table I. During this first 
stage, while all the substance still is water, sensibly all the heat 
that is supplied goes to increase the stock of internal energy 
which the fluid possesses, for the amount of external work done 
through the expansion of the water is negligibly small. 

68. Latent Heat of Steam. During the second stage 
water at temperature t is changing into steam at temperature t 
Much heat is required to produce this change in physical state, 
although the temperature of the substance does not alter. The 
heat taking in during this process is called the latent heat of 
steam : in other words the latent heat of steam is defined as the 
amount of heat which is absorbed by 1 lb. of water while it 
changes into 1 lb. of steam under constant pressure, the water 
having been previously heated up to the temperature at which 
steam is formed. We shall denote the latent heat by L. The 
value of L depends on the particular pressure at which the change 
takes place, Regnault's experiments showing that the latent 
heat of steam is less at high pressures than at low pressures. A 
formula for L derived from the results of Regnault's experiments 
is given in the next paragraph. 

Part of the heat taken in during this second stage is spent in 
doing external work, since the piston rises against the constant 
pressure of P lbs. per square foot. It is only the remainder of 
the so-called latent heat L that goes to increase the internal 
energy of the fluid. The amount spent in doing external work is 
equal to P multiplied by the change of volume which takes place 
as the water is converted into steam. 

The volume of 1 lb. of water, at such temperatures as are 
usual in steam-engines, is nearly 0*017 cubic feet. The ex- 
ternal work done during the production of 1 lb. of steam under 
constant pressure P is therefore 

External work = P(F- 0-017) (4). 



This is the measure of the external work in foot-pounds. It 
may of course be expressed in thermal units by dividing by J, 

69. Total heat of steam. Adding together the heat taken 

in during the first and second stages of th^ imaginary experiment 

we have a quantity designated by H and called the total heat of 

saturated steam : — 

H^h + L (5). 

In other words, the total heat of steam is the amount of heat 
required to raise lib. of water from the standard temperature 
(32° F.) to the temperature of evaporation and evaporate it there 
under constant pressure. Regnault's values of H are given in the 
fourth column of Table I. They are very accurately expressed 
(in thermal units) by the formula 

fi'=1082 + 0-305i (6). 

A similar formula gives approximate values of L, exact enough 
for use in practical calculations : — 

i = 1114-0-7« (7). 

It is, however, generally more convenient to find L fix>m the 
table, which is readily done, since 

It follows from these definitions that the whole heat taken 
in during the formation of lib. of steam, when formed under 
constant pressure from water at any temperature to, is fi^ — Aq, 
where ho corresponds to to. 

To take a numerical example, suppose that steam is formed in 
a boiler ajb an absolute pressure of 115 pounds per square inch, the 
feed water being supplied at 100° F. Here Ao is 100 - 32 or 68 
thermal units. By the table the temperature of the steam t is 
338° F. and H is 1185. The same value of f is obtained by using 
the formula 

^^ = 1082 + 0-305x338. 

Hence the heat taken up by each pound of water in the boiler in 
first being heated to the boiler temperature and then converted 
into steam is 

1185 - 68 or 1117 thermal units. 

It is scarcely necessary to add that when steam is condensed 
under constant pressure an amount of heat equal to X is given out 


during the change of state from steam to water. Begnault's 
experiments on the latent heat of steam were in fact made by 
observing the heat given out when steam from a boiler was led to 
a calorimeter and was there condensed. 

60. Internal energy of steam. Of the whole latent heat 
of steam i, the part PiV— 0017) is, as has been said above, spent 
in doing external work. The remainder, namely (in foot-pounds) 

JX«P(F- 0-017), 

is the increase of internal energy which the substance undergoes 
during conversion from water at t into steam at t This quantity, 
for which it is sometimes convenient to have a separate symbol, 
will be denoted by p in thermal units, or Jp in foot-pounds. In 
dealing with the heat required to produce steam we adopted the 
state of water at 32° F. as an arbitrary starting-point from which 
to reckon the reception of heat. In the same way it is convenient 
to use this arbitrary starting-point in reckoning what may be 
called the internal energy of the substance, which is the excess of 
the heat taken in over the external work done by the substance 
during its reception of heat. Thus the internal energy / of 1 lb. 
of saturated steam at pressure P is equal to the total heat H, less 
that part of the total heat which is spent in doing external work, 
or (in foot-pounds) 


or /=i-hA-P(F-0-017)/J=A-h/> (8). 

The notion of internal energy is useful in calculating the heat 
taken in or rejected by steam during any stage of its expansion or 
compression in an engine. When any working substance passes 
from one condition to another, its gain or loss of heat is determined 
by the equation 

Heat taken in = increase of internal energy -H external work. 
Any of the terms of this equation may be negative ; the last term 
is negative when work is done upon the substance instead of 
by it 

61. Formation of steam otherwise than under constant 
pressure. The same equation gives a means of finding the 
amount of heat required to form steam under any assigned con- 
ditions, in place of the condition assumed at the beginning of this 


chapter, where the formation of steam under constant pressure 
was considereA Whatever be the condition as to pressure under 
which the process of formation is carried on, the total heat required 
is the sum of the internal energy of the steam when formed and 
the work done by the expanding fluid during the process. Thus 
in general 

Heat of formation = /+j/PdF (9), 

in thermal units, the limits of integration being the final volume of 
the steam and the original volume of the water. When saturated 
steam is formed in a closed vessel of constant volume no external 
work is done ; the heat of formation is then equal to the internal 
energy /, and is less than the total heat of formation (H) of steam 
when formed at a constant pressure equal to the pressure finally 
reached in the vessel, by the quantity P(F— 0017). 

62. Wet steam. In calculations which relate to the action 
of steam in engines we have generally to deal, not with dry 
saturated steam, but with wet steam, or steam which either carries 
in suspension, or is otherwise mixed with, a greater or less 
proportion of water. In every such mixture the steam and water 
have the same temperature, and the steam is saturated. The 
dryness of wet steam is measured by the proportion q of dry 
steam in each pound of the mixed substance. When the dryness 
is known it is easy to determine the other physical constants : thus — 

Latent heat of 1 lb. of wet steam = qL ; 
Total heat of 1 lb. of wet steam = A + g/i ; 
Volume of 1 lb. of wet steam = 2 F+ (1 - g) 0-017 

= gF very nearly, 
unless the steam is so wet as to consist mainly of water ; 
Internal energy of 1 lb. of wet steam — h + qp. 

63. Superheated steam. Steam is superheated when its 
temperature is raised, in any manner, above the temperature which 
corresponds to saturation at the actual pressure. When much 
superheated, steam behaves like a perfect gas, and (to use Rankine's 
term) may be called steam gas. It then follows the equation 

PF== 85-5t, 
and the specific heat at constant pressure, Kpy is about 0*48 


thermal unit or 373 foot-poands. At very low temperatures steam 
approximates closely to the condition of a perfect gas when very 
slightly superheated, and even when saturated ; at high tempera- 
tures a much greater amount of superheating is necessary to bring 
about an approach to the perfectly gaseous state. The total 
heat required for the production of superheated steam under any 
constant pressure, when the superheating is sufficient to bring the 
steam to the state of steam gas, may therefore be reckoned by 
taking the total heat of saturated steam at a low temperature and 
adding to it the product of Kp into the excess of temperature 
above that. Thus Bankine, treating saturated steam at 32*^ F. as 
a gas, gives the formula 

J' = 1092 + 0-48(«'-32) 

to express the heat of formation (under any constant pressure) of 
superheated steam, at any temperature if which is so much above 
the temperature of saturation con:esponding to the actual pressure 
that the steam may be treated as a nearly perfect gas. Calculated 
from its chemical composition, the density of steam gas should be 
0'622 times that of air at the same pressure and temperature. The 
value of 7 or Kp/Kv for steam gas is 1*3. These constants and 
formulas, dealing as they do with steam which is so highly super- 
heated as to be perfectly gaseous, do not apply to high-pressure 
steam that is heated but little above its temperature of saturation. 
The relation of pressure to volume and temperature in the region 
which lies between the saturated and the perfectly gaseous state 
has been experimented on by Hirn\ and formulas which are ap- 
plicable with more or less accuracy to steam in either the saturated 
or superheated condition have been devised by Him, Zeuner*, 
Ritter', and others. 

64. Isothermal Lines fbr Steam. The expansion of volume 
which occurs during the conversion of water into steam under 
constant pressure — the second stage of the process described in 
§ 53 — is isothermal. From what has been already said it is 
obvious that steam, or any other saturated vapour, can be expanded 
or compressed isothermally only when wet, and that evaporation 

^ TMorie Mieanique de la Chaleur. Part 6, Vol. n. 
3 ZUchr. d. Vereins deiUseher Ingenieure, vol. zi. 

* Wied. Ann.t 1S78. For a disonssion of several of these fommlas, see a paper 
by H. Dyer, Tram. Intt, ofEngineen and Shipbuilden in Scotland, 1885. 


(in the one case) or condensation (in the other) must accompany 
the process. Isothermal lines for a working substance which 
consists of a liquid and its vapour are straight lines of uniform 

66. Adlabatic Lines fbr Steam. The form of adiabatic lines 
for substances of the kind just described depends not only on the 
particular fluid, but also on the proportion of liquid to vapour in 
the mixture. In the case of steam, it has been shown by Rankine 
and Clausius that if steam initially dry be allowed to expand 
adiabatically it becomes wet, and if initially wet (unless very wet^) 
it becomes wetter. To keep steam dry while it expands some heat 
must be supplied during the process of expansion. If the expan- 
sion is adiabatic, so that no heat reaches the expanding fluid, 
a part of the steam is condensed, forming either minute particles 
of water suspended throughout the mass or a dew upon the 
surfigwe of the containing vessel The temperature and pressure 
fall; and, as that part of the substance which remains uncon- 
densed is saturated, the relation of pressure to temperature 
throughout the expansion is that which holds for saturated steam. 
The following formula, a proof of which will be given in the next 
chapter (§ 80 below), serves to calculate the extent to which 
condensation takes place during adiabatic expansion, and so allows 
the relation of pressure to volume to be determined. 

Before expansion, let the initial dryness of the steam be ^i and 
its absolute temperature Ti. Then, if it expand adiabatically 
until its temperature falls to any value r, its dryness after expan- 
sion is 

'-i(^+"*5) : <"> 

Li and L are the latent heats (in thermal units) of 1 lb. of steam 
before and after expansion respectively. When the steam is dry 
to begin with, ji — 1. 

This formula, which is applicable with proper values of L to 
any vapour, may be called the equation of adiabatic expansion or 

^ When the miztnxe contains a very large proportion of water to begin with, 
adiabatic expansion tends to dry it by causing some of the water to evaporate under 
the reduced pressure which results from the expansion. In the next chapter a 
graphic method is described of investigating the changes of dryness that are 
produced by adiabatic expansion, and this may readily be applied to investigate 
whether the mixture wiU become drier or wetter in any given case. 


compression. It does not directly give the relation of pressure to 
volume, but it allows the drjmess at any stage of the process to be 
calculated, and from that (together with the fact that the part 
which remains in the condition of vapour is saturated) it is easy 
to find the volume which the mixture will fill when its pressure 
has changed to any assigned value. An example may help to make 
this clear. Suppose for instance that originally dry saturated steam 
at an absolute pressure of 115*1 pounds per square inch is made to 
expand adiabatically. Its original volume per lb. (taken from 
Table I.) is 3-843 cubic feet and its temperature is 338° F. We 
wish to find the relation of pressure to volume at any stage in the 
expansion. Take any value of the pressure reached by expansion, 
say 20*8 pounds per square inch absolute. The corresponding 
temperature is 230° F. by the table. This gives, for the values of 
quantities in the adiabatic equation (10), 

y, = l, Ti = 338 + 461 = 799 
T = 230 + 461 = 691, 
A = jg; - Ai = 11850 - 308-7 = 876-3 
i = J? - A = 11521 - 198-7 = 953-4. 

„ 691 /I X 876-3 . , 799\ 

^^^^^ «=95F4l-T99- + ^"»-69lj 

= 0-900. 
This means that by the time the pressure has fallen to 20-8 
pounds per sq. inch just one-tenth of the originally dry steam has 
become condensed into water. The volume occupied by that part 
of the substance which is still in the state of steam is yFper lb. 
of the mixture, where V is the volume of 1 lb. of dry steam at the 
pressure of 20*8 lbs. per sq. inch. Taking the value of V given in 
the table, namely 19*18 cubic feet, qV is 17*26 cubic feet. To 
obtain the whole volume of 1 lb. of the working substance we 
have in strictness to add to this the volume occupied by that part 
which has been converted into water, namely by the fraction of a 
lb. which is represented by 1 — q. But this is only 0-1 lb., and its 
volume is 0*1 x '0017 or -00017 cubic feet — a quantity entirely 
negligible in comparison with the volume occupied by the still 
nncondensed steam. We conclude that 17*26 cubic feet is the 
volume of the mixture (per lb.) when its pressure has fallen to 
20*8 pounds per square inch by adiabatic expansion; in other 
words these numbers determine one point on the adiabatic line 


which begins with dry steam at a pressure of 115*1 pounds per 
square inch. 

In the same way we may go on to find as many points on an 
adiabatic line as we please, by taking a series of pressures, each 
lower than the initial pressure, and finding q for each and from it 
the volume v, which in ordinary cases is practically equal to qV. 
We use V here to designate the volume of 1 lb. of the mixture, V 
being the volume which 1 lb. of satui-ated steam would occupy at 
the same pressure and temperature. 

The steam may be wet to begin with, and if ji have a value 
much less than unity it will be found on working out examples 
that q may turn out greater than q^. This means that in very 
wet steam adiabatic expansion may reduce the amount of water as 
the net result of two opposing actions : as the temperature falls 
during expansion part of the steam initially present becomes 
condensed ; on the other hand part of the water initially present 
becomes evaporated because its initial temperature is higher than 
the temperature which the mixture takes as it expands. With 
very wet steam the result may be on the whole to make the 
mixture become drier. An extreme case occurs when all the 
substance is in the state of water to begin with. Then if adia- 
batic expansion be allowed to take place steam is formed, and the 
equation (9) may be applied, by writing ji = 0, to find how much of 
the water will be evaporated when the pressure, or the temperature, 
has fallen to any assigned value. 

66. Formula connecting pressure with volume in the 
adiabatic expansion of steam. Adiabatic curves for steam, 
whether initially dry or wet, may be calculated in the way that 
has just been explained, and may then be represented by empirical 
equations of the form 

Pv^ = constant, 

by choosing such values for the index n as will give curves approxi- 
mating closely to the actual adiabatic curve. A formula of this 
kind is especially useful for application to cases where the data 
are the initial pressure and the ratio of expansion r, and it is 
required to find the pressure after expansion. To find P when 
the substance has expanded to r times its initial volume, 

p-^" <">• 


The index n has a value which depends on ji, the initial degree 
of dryness of the steam. According to the calculations of Zeuner ^ 
n = 1'035 + O'lji, so that for 

gi=l 0-95 0-9 0-85 0-8 075 0-7 

n = 1-135 1-130 1125 1120 1-115 1110 1105. 

When it is desired to draw an adiabatic curve for expanding 
steam, that value of n must be chosen which refers to the degree 
of dryness at the beginning of the expansion. Bankine gave for 
this index the value J^, which is too small if the steam be initially 
dry. It would apply to steam containing about 25 per cent, of 
water at the beginning of its expansion. We shall see later that 
the expansion of steam in an actual engine is by no means 
adiabatic, on account of the transfer of heat which goes on 
between the working fluid and the metal of the cylinder and 

67. Camot'8 cycle with steam for working substance. 

We are now in a position to study the action of a heat-engine 
employing water and steam (or any other liquid and its vapour) 
as the working substance. To simplify the first consideration of 
the subject as far as possible, let it be supposed that we have, as 
before, a long cylinder composed of non-conducting material 
except at the base, and fitted with a non-conducting piston ; also 
a source of heat A at some temperature Ti ; a receiver of heat, or 
as we may now call it, a condenser, C, at some lower temperature 
Ta ; and also a non-conducting cover 5 (as in § 41). Then Camot's 
cycle of operations can be performed as follows. To fix the ideas, 
suppose that there is 1 lb. of water in the cylinder to begin with, 
at the temperature Ti ; — 

(1) Apply -4, and allow the piston to rise under the constant 
pressure Pi which corresponds to the temperature Ti. The water 
will take in heat and be converted into steam, expanding 
isothermally at the temperature Tj. This part of the operation 
is shown by the line ab in fig. 14. . 

(2) Remove A and apply \B. Allow the expansion to con- 
tinue adiabatically (&c), with falling pressure, until the tempera- 

1 GrundzUge der Meeh. Wdrmetheorie, p. 342. See also Grashof, RenUtate aus 
der Meeh, Wdrmetheorie, § 87. In the adiabatio compression of wet steam 
n=l*0S4+0'llgi, where q^ is the dryness at the beginning of compression. 



ture falls to r^ The pressure will then be Pj, namely the 
pressure which corresponds in the steam table to r, which is the 
temperature of the cold body (7. 

Fig. 14. Camot*s Cyde with water and steam for working substance. 

(3) Bemove B, apply C, and compress. Steam is condensed 
by rejecting heat to C, The action is isothermal, and the pressure 
remains P,. Let this be continued until a certain point d is 
reached, after which adiabatic compression will complete the cycle. 

(4) Remove G and apply B. Continue the compression, 
which is now adiabatic. If the point d has been rightly chosen, 
this will complete the cycle by restoring the working fluid to the 
state of water at temperature Tj. 

The indicator diagram for the cycle is drawn in fig. 14, the 
lines be and da having been calculated by the help of the equations 
in §§ 65 and 66, for a particular example, in which jpi = 90 lb. per 
square inch (ti = 781), and the expansion is continued down to 
the pressure of the atmosphere, 14*7 lb. per square inch (Ta= 673). 


Since the process is reversible, and since heat is taken in 
only at Tx and rejected only at tj, the efficiency is 

Ti - T, 

The heat taken in per lb. of the fluid is L^, and the work done is 


Tx ' 

a result which may be used to check the calculation of the lines 
in the diagram by comparing it with the area which they enclose. 
It will be seen that the whole operation is strictly reversible in 
the thermodynamic sense. 

Instead of supposing the working substance to consist wholly 
of water at a and wholly of steam at 6, the operation ah might be 
taken to represent the partial evaporation of what was originally a 
mixture of steam and water. The heat taken in would then be 
(?ft "■ ?a) L, and as the cycle would still be reversible the area of the 
diagram would be 


68. EflBlclency of a perfect steam-engine. Iiimlts of 
temperature. If the action here described could be realized in 
practice, we should have a thermodynamically perfect steam- 
engine using saturated steam. Like any other perfect heat-engine 
an ideal engine of this kind has an efficiency which depends upon 
the temperatures between which it works, and upon nothing else. 
The fraction of the heat supplied to it which such an engine 
would convert into work would depend simply on the two tempera- 
tures, and therefore on the pressures, at which the steam was 
produced and condensed respectively. 

It is interesting therefore to consider what are the limits of 
temperature between which steam-engines may be made to work. 
The temperature of condensation is limited by the consideration 
that there must be an abundant supply of some substance to 
absorb the rejected heat ; water is actually used for this purpose, 
so that r, has for its lower limit the temperature of the available 

To the higher temperature ti and pressure P^ a practical limit 
is set by the mechanical difficulties, with regard to strength and 


to lubrication, which attend the use of high-pressure steam. By 
a very special construction of engine and boiler Mr L. Perkins has 
been able to use steam with a pressure as high as 500 lbs. per 
square inch; with engines of the usual construction the value 
ranges from about 200 lbs. downwards. 

This means that the upper limit of temperature, so far as the 
steam is concerned, is barely 400"* F. A steam-engine, therefore, 
under the most favourable conditions, comes very far short of 
taking full advantage of the high temperature at which heat is 
produced in the combustion of coaL In a thermodynamic sense 
the worst thing about a steam-engine is the irreversible drop of 
temperature between the furnace and the boiler. 

If the temperature of condensation be taken as 60*" F., as a 
lower limit, the efficiency of a perfect steam-engine, using satu- 
rated steam, would depend on the value of Pi, the absolute 
pressure of production of the steam, as follows : — 

Perfect steam-engine, with condensation at 60° F., 
Pi in lbs. per square inch being 40 80 120 160 200 
Highest ideal efficiency ='284 '326 "350 '368 -381 

But it must not be supposed that these values of the efficiency 
are actually attained, or are even attainable. Many causes con- 
spire to prevent steam-engines from being thermodynamically 
perfect, and some of the causes of imperfection cannot be removed. 
These numbers will serve, however, as one standard of comparison 
in judging of the performance of actual engines, and as setting forth 
the advantage of high-pressure steam from the thermodynamic 
point of view. 

69. EflBlclency of an engine using steam non-expan- 
sively. As a contrast to the ideally perfect steam-engine of § 67 
we may next consider a cyclic action such as occurred in the early 
engines of Newcomen or Leupold, when steam was used non- 
expansively, — or rather, such an action as would have occurred in 
engines of this type had the cylinder been a perfect non-conductor 
of heat. In that case the volume of steam formed is equal to the 
volume swept through by the piston. We may represent the 
action of such an engine thus : 

(1) Apply the hot body A and evaporate the water as before 
at Pi. Heat taken in, per lb. of the working fluid, = ii. 



(2) Remove A and apply the cold body C. This at once 
condenses a part of the steam, and reduces the pressure to Pj. 

Fig. 16. 

(3) Compress at Pj, in contact with (7, till condensation is 
complete, and water at Tj is left. 

(4) Eemove B and apply A. This heats the water again to 
Ti and completes the cycle. Heat taken in = Aj — Ag. 

The indicator diagram for this series of operations is shown in 
fig. 15, where oe = Pi and oh^P^ 

Here the action is not reversible. To calculate the efficiency, 

Work done ^ (P, ~ P,) ( V^ - 0017 ) 
Heat taken in •/(Zi + Ai — Aj) 

The values of this will be found to range fi:om 0*067 to 0*072 for 
the values of Pj which are stated in § 68, when the temperature 
of condensation is 60°F, Contrast these numbers with the much 
higher efficiencies found in the last paragraph for a perfect steam- 
engine, following Camot's cycle. 

The efficiency of the actual Newcomen engine was much lower 
even than this calculation indicates, because in every stroke of the 
piston a large part of the steam entering the cylinder was at once 
condensed upon the sides, and the volume of steam which had to 
be formed in the boiler was therefore much greater than the 
volume swept through by the piston. 

70. Engine with separate organs. In the ideal engine 
represented in fig, 14 the functions of boiler, cylinder, and con- 
denser are combined in a single vessel ; but after what has been 
said in Chapter II. it is scarcely necessary to remark that, provided 



the working substance passes through the same cycle of operations 
it is indifferent whether these are performed in several vessels or 

Fio. 16. Organs of a Steam-Engine. 

in one. To approach a little more closely the conditions that hold 
in practice, we may think of the engine which performs the cycle 
of § 69 as consisting of a boiler A (fig. 16) kept at Ti, a non-con^ 
ducting cylinder and piston B, a surface condenser C kept at Tj, 
and a feed-pump D which restores the condensed water to the 
boiler. Then for every pound of steam supplied and used non- 
expansively as in § 69, we have 

work done on the piston =(Pi - P,) Fj ; 

but the amount of work which has to be expended in driving the 
feed-pump is (Pi - Pj) 0017. Deducting this, the net work done 
per lb. of steam is the same as before, and the heat taken in is 
also the same. An indicator diagram taken fi'om the cylinder 
would give the area efgh (fig. 15), where 

oe = Pi, ef^Vu oh^P^; 

an indicator diagram taken from the pump would give the nega- 
tive area hjie, where ei is the volume of the feed-water, or 0*017 
cub. ft. The difference between these two areas, namely, the area 
ifgh which is shaded in the figure, is the diagram of the complete 
cycle gone through by each pound of the working substance. In 
experimental measurements of the work done in steam-engines, 
only the action which occurs within the cylinder is shown on the 


indicator diagram. From this the work spent on the feed-pump 
is to be subtracted if we wish to make a rigorous determination 
of the thermodynamic eflBciency. If the feed-water be at any 
temperature Tq other than the temperature of condensation t,, it 
is clear that the heat taken in is -Hi — A^ instead of i/i — A,. 

71. How nearly may the procesi in a steam-engine be 
reversible P We have now to inquire how nearly, with the 
engine of fig. 16 (that is to say, with an engine in which the 
boiler and condenser are separate from the cylinder), we can 
approach the reversible cycle of § 67. The first stage of that cycle 
corresponds to the admission of steam from the boiler into the 
cylinder, for during admission of steam to the cylinder a corre- 
sponding quantity of steam is being formed in the boiler. Then 
the point known as the point of cut-off is reached, at which 
admission ceases, and the steam already in the cylinder is allowed 
to expand, exerting a diminishing pressure on the piston. This is 
the second stage, or the stage of expansion. The process of 
expansion may be carried on until the pressure fells to that of the 
condenser, in which case the expansion is said to be complete. At 
the end of the expansion release takes place, that is to say, 
communication is opened with the condenser. Then the return 
stroke begins, and a period termed the exha/ust occurs, that is to 
say, steam passes out of the cylinder, into the condenser, where it 
is condensed at pressure P„ which is felt as a Inick pressure 
opposing the return of the piston. So far, all has been essentially 
reversible, and identical with the corresponding parts of Camot's 

But we cannot complete the cycle as Camot's cycle was com- 
pleted. The existence of a separate condenser makes the fourth 
stage, that of adiabatic compression, impracticable, and the best 
we can do is to continue the exhaust until condensation is com- 
plete, and then return the condensed water to the boiler by means 
of the feed-pump. 

It is true that we may, and in actual practice do, stop the 
exhaust before the return stroke is complete, and compress that 
portion of the steam which remains below the piston, but this 
does not materially affect the thermodjnmmic efSciency ; it is done 
partly for mechanical reasons, and partly to avoid loss of power 
through clearance (see Chap. V.). In the present instance it is 
£. 6 



supposed that there is no clearance, in which case this compression 
is out of the question. The indicator diagram given by a cylinder 
in which steam goes through the action described above is shown 
to scale in fig. 17 for a particular example, in which it is supposed 
that dry saturated steam is admitted to the cylinder at an absolute 
pressure of 90 lbs. per square inch, and is then expanded adiabati- 
cally to twelve times its original volume. This brings it down to 

5 6 7 


Fig. 17. Ideal Indicator Diagram for Steam used expansively. 

a pressure of 5*4 lbs. per square inch, at which pressure it is dis- 
charged to the condenser. As we have assumed the cylinder to 
be non-conducting, and the steam to be initially dry, the expansion 
curve is calculated by the formula Pi;i-i» = constant (§ 66). The 
advantage of expansion is obvious, that part of the diagram which 
lies under the curve being so much clear gain, as compared with 
the case dealt with in § 69. 

To calculate the performance, we have 

Work done per lb. during admission = PiFi ; 

„ „ during expansion to volume rVi= ^ ^ _i' — ^ 

Work spent during return stroke ^P^rVii 

„ „ on the feed-pump = (Pi — Pj) 0*017 ; 
Heat taken in = J?i — A©. 



Then, by comparing the net amount of work done with the heat 
taken in we may find the efficiency. Another method of calcula- 
ting the efficiency in this cycle of operations will be given in the 
next chapter. 

In the above example the expansion is complete, that is to say 
the substance is allowed to expand until its temperature falls to 
that of the condenser or cold body into which heat is to be 

When the expansion is incomplete, as it generally is in practice, 
the expression given above for the work done during expansion 
still applies if we understand P, to be the pressure at the end of 
expansion, while the work spent on the steam during the back- 
stroke is P^rFi and that spent on the feed-pump is (Pi — P^) 0*017, 
Pi, being the back-pressure. Incomplete expansion is illustrated 
by fig. 18, where the steam is supposed to escape after expanding 

Fig. 18. Incomplete expansion. 

to five times its initial volume. It results simply in a loss of the 
work which is represented by the difference of areas between 
this and the last figure. 

It is easy to extend these calculations to cases where the 
steam, instead of being initially dry, is supposed to have any 
assigned degree of wetness. The efficiency which is calculated in 
this way, which for the present purpose may be called the theo- 



retical efficiency corresponding to the assumed conditions of 
working, is always less than the ideal highest efficiency of a 
perfect engine working between the same limits of temperature. 
This is because of the absence of the compression which formed the 
fourth stage in Carnot's cycle, and had the effect of bringing the 
temperature up to the top of the range before the substance began 
to take in heat. Without compression some of the heat is taken 
in at temperatures below the highest temperature Ti, and any heat 
taken in at a lower temperature cannot contribute so much work 
as if it had been taken in at Ti. But even the theoretical effici- 
ency working in this way without compression, short as it £etlls of 
the ideal of a perfect engine, is &r greater than can be realized 
in praqtice when the same boiler and condenser temperatures are 
used, and the same ratio of expansion. The reasons for this will 
be considered in Chapter V. ; at present the fact is mentioned to 
guard the reader from supposing that the results which the above 
formulas give apply to actual engines. 

Meanwhile, we proceed to give in the next chapter some further 
developments and applications of thermodynamic theory, especially 
in relation to steam. 



72. Rankine's statement of the Second Law. Bankine, 
to whom with Clausius and Lord Kelvin is due the development 
of the theory of heat-engines from the point at which it was left by 
the " Reflexions'' of Oamot and the experiments of Joule, has, in 
his " Manual of the Steam-Engine and other Prime Movers/' stated 
the second law of thermodynamics in a form which is neither easy 
to understand, nor obvious, as an experimental result, when under- 
stood His statement runs : — ^ 

" If (the absolute temperature of any uniformly hot substance 
be divided into any number of equal parts, the effects of those 
parts in causing work to be performed are equal" 

To make this intelligible we may suppose that any quantity q 
of heat fix)m a source at temperature Ti is taken by the first of a 
series of perfect heat-engines, and that this engine rejects heat at 
a temperature t, less than Ti by a certain interval At. Let the 
heat so rejected by the first engine form the heat supply of a 
second perfect engine working from Tj to t, through an equal 
interval At; let the heat which it in turn rejects form the 
heat-supply of a third perfect engine working again through an 
equal interval from t, to T4 ; and so on. The efficiencies of the 
several engines are (by § 47) 

At At At . 

Tj Ta T, 

The amounts of heat supplied to them are 

T, T, « 

?.?-» J-,&c. 

Ti T, 


Hence the amount of work done by each engine is the •same, 

namely, q — . 

Thus Bankine's statement is to be understood as meaning that 
each of the equal intervals into which any range of temperature 
may be divided is equally effective in allowing work to be 
produced from heat when heat is made to pass, doing work in the 
most efficient possible way, through all the intervals from the top 
to the bottom of the range. 

73. Absolnte Temperature: Lord Kelvin's scale. In 

the preceding chapters we have been using the imaginary perfect 
gas thermometer as the means of framing a scale of temperatures. 
In other words our scale has been such that equal intervals of 
temperature are defined as those which correspond to equal 
amounts of expansion of a perfect gas under constant pressure. 
We have defined t by means of the formula F=ct, P being 
constant. And seeing that air behaves as a nearly perfect gas 
this scale is practically realised by the air thermometer. 

Starting from this definition of temperature we have found by 
an application of Camot's principle that a reversible engine 
working between a hot source A and cold receiver of heat G takes 
in from the source and gives out to the receiver quantities of heat 
Qji and Qc which are proportional to the absolute temperatures of 
the source and receiver respectively, as defined by reference to the 
perfect gas thermometer. 

Hence we might have defined temperature in a very different 
way and still have arrived at just the same scale. We might have 
said, let the temperatures of A and C be specified by two numbers 
which shall be proportional to the heat taken in and given out 
respectively by a reversible heat-engine when working with A for 
source and C for receiver of heat. This method of defining absolute 
temperature was proposed by Lord Kelvin. It gives a scale which 
is truly absolute in the sense of being independent of the proper- 
ties of any gas or other substance, real or imaginary. The scale so 
obtained coincides with the scale of the perfect gas thermometer. 

Lord Kelvin's method of devising a scale of absolute tempera- 
tures may also be put in a somewhat different &shion, thus: — 
Starting with any arbitrary temperature let a series of intervals 
be taken such that equal amounts of work will be done by every 


one of a series of reversible engines, each working with one of 
these intervals for its range and each handing on to the engine 
below it the heat which it rejects (so that the heat rejected by the 
first forms the supply of the second, and so on). Then call these 
intervals equal. This is only another way of putting the definition 
of absolute temperature which has just been quoted : it is sug- 
gested by what has been said in the last paragraph SLJaout 
Bankine's statement of the Second Law. 

The scale of the actual air thermometer would be in perfect 
agreement with Lord Kelvin's absolute scale if the laws stated in 
Chapter II. were rigorously true of air, namely Regnault's law 
according to which the specific heat at constant pressure is 
constant (§ 33), and Joule's law according to which there is no 
change of temperature when a gas expands without doing external 
work and without receiving or rejecting heat (§ 34). The experi- 
ments by which Joule established his law have been already 
described. Subsequent experiments of a more searching kind, 
devised by Lord Kelvin, and carried out by him in conjunction 
with Joule, in which air was forced slowly through a porous plug to 
see whether its temperature became changed, have shown that air 
does not conform with perfect exactness to Joule's law* ; but the 
deviations are so slight that for all practical purposes the scale of 
the air thermometer may be taken as agreeing with the absolute 

Actual air thermometers may be made for use in two ways : In 
one the pressure is kept constant and the volume is allowed to ex- 
pand or contract as the temperature varies ; in the other the volume 
is kept constant by adapting the pressure to the temperature which 
is being measured, and the temperature is then taken to be 
proportional to the pressure. The air must be perfectly dry: if 
there is any water vapour in it the volume in the one case or the 
pressure on the other may be £ax from proportional to the tempera- 

74. Calculation of the Density of Saturated SteanL 

In our account of the physical properties of saturated steam it 
was mentioned that the volumes of I lb. stated in the third column 

^ See Lord Eelyin's Collected Papers, Vol. i. p. 383. 

' For a oomparison hj Bowland based on the experiments of Joole and Lord 
Kelvin, see Proceedings of the American Academy, 1879, also Professor Peabody's 
ThermodynandcM of the Steam Engine, Chapter ti. 


of Table I. were not found by direct experiment, but were cal- 
culated firom other known properties. To explain how this is done 
we may revert to the ideally perfect steam-engine of § 67, in which 
Camot's cycle is followed with water and steam for working 
substance. We saw that this gave a indicator diagram (fig. 14) 
with two lines of uniform pressure (isothermals) connected by two 
adiabatic curves. The heat taken in was L per lb. of working 
substance, and since the engine was reversible its efficiency was 

fix)m which it followed that the work done, or the area of the 
diagram, was 


This is in thermal units : to reduce it to foot-pounds we multiply 
by J. Now suppose that the engine works between two tempera- 
tures which differ by only a very small amount. We may call the 
temperatures t and t — St, St being the small interval through 
which the engine works. The above expression for the work done 
becomes (in foot-pounds) 



The indicator diagram is now a long narrow strip (fig. 19). 
Its length a6 is F— it;, F being the volume of 1 lb. of steam and 



Fio. 19. 

w the volume of 1 lb. of water, or say 0*017 cubic feet. Its height 
is BP, where BP is the difference between the pressure in ab and 
that in cd. In other words, since the steam is saturated in cc2 as 
well as in ob, SP is the difference in the pressure of saturated 


steam due to the difference in temperature St. When BF is made 
very small, the area of the diagram becomes more and more 
nearly equal to the product of the length by the height, namely 
SP(V—w). This is equal to the work done, whence 

8P(r-w) = ^^ (1). 


This equation is only approximate when the interval 8t (or SP) 
is a small finite interval In the limit, when the interval is made 
indefinitely small, it becomes exact and may then be written 

^-""'-VdP (2>' 

^ being the rate at which the temperature of saturated steam 

alters relatively to the pressure when the temperature is t. 
Thus we have the equation 

XT JL dr 

T dP 

as a means of calculating the volume of 1 lb. of steam when the 

values of L and of -rp for various temperatures are known. 

Regnault's experiments determined Z, and by giving the relation of 

P to r they also gave data from which it is easy to find ~jp either 

by measuring the slope of a tangent to the curve of t and P or by 
differentiating a formula such as equation (1) of § 55 which ex- 
presses the experimental relation between these two quantities. 
It was in this way that the values of V in the Table were 

The advantage of the method is that L and jp can be 

measured more accurately than V could itself be measured and 
thus the values of V obtained indirectly from them are more 
likely to be right than those obtained by direct experiment. The 
formula shows that the numbers found in this way depend on J, 
and are nearly proportional to it, since w is small ; and hence, as 
has been remarked before, the numbers given in the third column 
of the Table have required alteration from those given by Rankine, 
because 778 is accepted as the mechanical equivalent of heat 
instead of 772*. 


76. Eztension of the above reralt to other changes 
of phsrsical state. In equation (2), above, the left-hand side 
is positive, since V the volume of 1 lb. of steam is greater 
than w the volume of 1 lb. of water. The right-hand, side 

must also be positive and hence it is that jp is positive, or 

in other words that increasing the pressure under which steam is 

formed raises the boiling point. The equation might evidently 

be applied in the reverse way to that indicated above (for finding 

V) ; in other words, if the amount by which the volume increases 

when water changes into steam were given we might employ that 

to calculate -rp , the rate at which the boiling point is raised by 

increase of pressure. 

Further, the reasoning by which this equation was arrived at 
was perfectly general and was in no way restricted to the case 
of steam. The engine whose indicator diagram is sketched in 
fig. 19 might have anything for working substance, the isothermal 
line of the first operation, during which heat is taken in, repre- 
senting in the most general way the change of volume which 
occurs while any working substance changes its physical state. 
In the example already dealt with the change is from liquid to 
vapour. But we might begin with a solid substance previously 
raised to the temperature r at which it begins to melt and let the 
first stage in the cycle consist in the expansion of the substance 
while it passes from the solid to the liquid state, the substance 
doing external work by overcoming a constant pressure as it 
expands. All the steps in the argument remain unaffected, and 
hence the equation may be written thus with reference to any 
transformation of state on the part of any substance, 

U-W^^ ^ (3), 

where V is the volume of unit mass of the substance in the 
original state, U is the volume after the transformation has taken 
place, X is the heat absorbed while the transformation is going on 
(the latent heat of fusion or of evaporation as the case may be), 

and -Tp is the rate at which the temperature of the transformation 

(say the melting-point or the boiling-point) is affected by altering 
the pressure under which the change of state occurs. 


If a solid body expands on melting, U is greater than U and 
consequently -rp must be positive : in other words the melting- 
point will in that case be raised by applying pressure. 

On the other hand if the substance contracts on melting, 
IT— IT is negative and t must then decrease relatively to P, that 
is to say, the melting-point is then lowered by applyhig pressure. 
This is the case with ice. From the known amount by which ice 
contracts when it melts James Thomson (in 1849) first applied 
this method of reasoning to show that the melting-point of ice 
must be lowered to a definite extent when the ice is melted under 
any assigned pressure, and the result was afterwards verified by an 
experiment of his brother, Lord Kelvin. The amount by which 
the melting-point is lowered is about 0*01 35** F. for each atmo- 
sphere of pressured 

76. Drying of steam by throttling or wire-drawing. 

When dry steam expands without doing work and without receiv- 
ing or rejecting heat it becomes superheated ; and if wet to begin 
it becomes drier. This is because the total heat of steam (fl) is 
less at low pressure than at high. Suppose for instance that 
steam is flowing through a small pipe or orifice from a chamber 
where the pressure is Pi to another where it is P^ Such an 
action happens in steam-engines in the movement of steam 
through contracted pipes and passages between the boiler and the 
valve chest : the steam becomes reduced in pressure and is said to 
be throttled or "wire-drawn." Eddies are formed in rushing 
through the constricted openings and the energy expended in 
forming them is firittered down into heat as the eddies subside. 
To calculate the amount of drying, in the case of steam that 
is initially wet, we have (if no heat enters or leaves the fluid) 

qiL^ + hy — q^L^ + K 
where the suffixes 1 and 2 refer to the condition before and after 
throttling respectively. It is assumed that a steady condition 
exists before and also after the throttling and that the chambers 
are large, so that the stream of steam has no kinetic energy worth 
taking account of either before it passes the orifice or after it 
has passed and the eddies have subsided. From this 

*'" L, ' 

^ See Lord Kelvin's Collected Papen, Vol. i. p. 156 and p. 1S6. 


In the same way dry steam escaping at high pressure from a 
boiler into the atmosphere is superheated at a little distance from 
the orifice ; further off it becomes condensed by loss of heat to 
the air. 

77. Engine receiving heat at various temperatttres. 

In Camot's cycle it was assumed that the working substance 
took all its heat in at the higher limit of temperature Ti. Im- 
portant cases arise in which heat is taken in partly at one 
and partly at other temperatures in a single cycle of operations. 
With regard to every such quantity of heat the result still applies 
that the greatest fraction that can be converted into work under 
ideally favourable conditions is represented by the difference 
between its temperatures of reception and rejection, divided by 
the absolute temperature of rejection. 

Thus if Qi represents that part of the whole heat which is 
taken in at Ti, and Q, represents what is taken in at some other 
temperature Tj, Q, at t, and so on, and if Tq be the temperature at 
which the engine rejects heat, the whole work done, if the 
processes within the engine are reversible, 

^^M[LZLl<L) + e?iliI^ ...(4). 

It is perhaps worth while to point out the analogy here to the 
supposititious case of a water-wheel working by gravity and 
receiving water into its buckets at different heights above the 
level at which water is discharged frt>m them. Let Mi, M^ and 
so on be the quantities of water received at heights l^, l^ etc. above 
any datum level and let ^o be the height above the same datum 
level at which the water leaves the wheel If the wheel is per- 
fectly efficient (and here again the test of perfect efficiency is 
reversibility) the work done is 

Comparing the two cases we see that the quantity — is the 

analogue in the heat-engine of M^ in the water-wheel and so on. 
The amount of work which can be got out of a given quantity of 
heat by letting it down to an assigned level of temperature is not 
simply proportional to the product of the quantity of heat by the 

fall of temperature, but to the product of — by the fall of 



temperature. On the strength of this analogy Zeuner has called 
the quantity — the " heat weight" of a quantity of heat Q obtain- 
able at a temperature r. 

Another way of expressing the matter has a wider application. 
Let the engine as before take in quantities of heat represented by 
Qu Q2, Qz etc. at Ti, Ts, Tj and let ^ Qo represent the heat rejected 
at To, the negative sign being used to distinguish heat rejected 
from heat received. Then by the principle that in a reversible 
cycle the heat rejected is to the heat taken in as the absolute 
temperature of rejection is to the absolute temperature of reception, 
we have 


fix)m which 

2^ = (5), 

when the summation is effected all round the cycle. It is clear 
that this result may be at once extended to cases where heat is 
given out at various temperatures as well as taken in at various 
temperatures, Q being taken positive or negative according as heat 
is being received or rejected. 

In cases where changes of temperature are going on continuously 
while heat is being taken in or given out, we cannot divide the 
reception or rejection of heat into a limited number of steps, as 
has been done above. But the equation may be adapted to this 
most general case by writing it 

m-o (6), 


integration being performed round the whole cycle. 

78. Application to the case of a steam-engine working 
without compressionp but with complete adiabatic expan- 
sion. In § 71 we considered the action of an ideal steam-engine 
in which the steam formed at Ti was expanded adiabatically and 
fully, that is to say, down to the pressure corresponding to Ts the 
temperature of the condenser, and was then condensed, the con- 
densed water being then restored to the boiler by a feed-pump 
and thus heated again to Ti to complete the cycle. This cycle is 
specially important in the discussion of steam-engines because it 


represents the ideally best performance of an engine which uses a 
feed-pump to return the condensed water directly from the con- 
denser to the boiler, namely the performance which such an engine 
might achieve provided the expansion were complete, so that there 
should be no sudden drop of pressure at release, and provided the 
pylinder and piston were perfect non-conductors. The efficiency 
in this cycle falls short of the value 


because in the fourth stage of the cycle the working substance has 
its temperature raised from t, to Ti not by adiabatic compression, 
as in Camot's cycle (§ 67), but by being brought into contact 
with the contents of the boiler, which are kept at Ti. Conse- 
quently heat enters it in this stage by a non-reversible process : 
in all other respects however the cycle is reversible. 

But we may regard this as a strictly reversible cycle if we 
think of the feed-water as taking up its heat by infinitesimal 
instalments at a series of temperatures ranging from Tj up to Tj 
from a series of imaginary sources each of which has the same 
temperature as the water when the water is brought into contact 
with it. One may realise this notion by thinking of the feed- 
pipe as passing through a heated channel the temperature of 
which is Ti close to the boiler and tapers down to Tj close to the 
condenser. Thus the feed-water would have its temperature 
raised gradually and would nowhere be brought into contact with 
a source at a temperature different from the temperature which it 
had itself then reached. With such an arrangement as this it is 
clear that the engine becomes a strictly reversible engine, receiv- 
ing portions of its heat, however, at various temperatures. But 
the action of the engine is in no way altered by this imaginary 
arrangement of the feed-pipe, nor is the total supply of heat in 
any way altered. The notion of gradual heating in the feed-pipe 
has been introduced merely to show that the cycle is a reversible 
cycle if we take account of the fact that heat is received not all 
at the top of the range of temperature, but partly at lower tem- 
peratures. Every part of the heat which the substance receives 
is used in the most efficient possible way, after it has been taken 
iuy so that the expression 


measures the efficiency of the transformation into work of each 
portion of the heat, r being the particular temperature at which 
the working substance happens to be when it takes in that portion 
of the heat. The only non-reversible feature in the action of this 
engine is the flow of heat from a source at Ti into the feed-water 
while the temperature of the feed- water is less than Tj ; and we get 
rid of this partial non-reversibility by taking as the temperature of 
reception of each portion of the heat that temperature which the 
working substance has when the portion in question was taken in. 
It will be evident that these remarks are of general application 
and that when this understanding is accepted both with regard to 
the temperatures of reception and rejection of heat, the process in 
any heat-engine is to be taken as reversible provided the expan- 
sions and compressions which occur in it are themselves reversible 
in the sense which has been explained in § 50. With a source 
of heat at a given temperature the heat can be turned to account 
most efficiently only when all the heat is taken in while the 
working substance is at that temperature, and it is only then that 

the greatest value of the efficiency, namely — , can be reached. 

But the engine may take in part of its supply of heat at tempera- 
tures below Ti and still act reversibly in the conversion of the 
heat so received into work, in which case the total efficiency 

will be less than -^ though the general formula is still 

applicable in respect of every separate portion of the heat, when 
proper values are assigned to t. 

The ideal steam-engine which we are now considering is a 
case in point. It takes in the greater part of its heat at Ti, but 
some is taken in at temperatures ranging between t, and Ti. 
So far as actions occurring within the engine are concerned it is 
reversible. The amount of heat it converts into work is therefore 
to be found by calculating 

< 8Q(t-t,) 

where SQ represents any part of the heat taken in and t the 
temperature at which it is taken in. The whole heat taken in, 
per lb. of working substance, is, first, ii, the latent heat, which is 
taken in at Ti and, second, the amount of heat which is required 
to raise the water from Tj to Ti, that is Aj — A,. Hence the 


whole amount of work done per lb. of working steam (expressed 
in thermal units) is 


^.dfe( T-^T,) ^A(T,-T,) 

which may be written 

Jht Jht "T Tl 

This gives F = Ai-A,-T,log.^ + ^^i^^^^^ (7), 

since dh may be taken as almost equal to dr, the specific heat of 
water being very nearly constant and equal to unity. We might 
for the same reason write A^— A^ = ti — Tj and express the result 

F = (T.-T,)(l + ^)-T,l0g.^^ (8). 

This is the greatest amount of work which can be done, per lb. of 
steam, under ideally favourable conditions by an engine which 
takes steam from a boiler at temperature ti and restores con- 
densed water to the boiler at temperature Tj. The result is 
interesting as affording a standard with which the performance of 
actual steam-engines may be compared (see Chapter V.) \ 

The efficiency of a steam-engine working in this ideally 
favourable manner, but without compression, is to be found by 
dividing the above expression for W by the heat taken in per lb, 
of steam, which is 

Li + hi — h^. 

As a numerical example, take the case of an ideal engine working 
in this way, receiving steam at an absolute pressure of 160 lbs. 
per sq. inch, and condensing it at 60° F., with complete adiabatic 
expansion from the top to the bottom of this range. Here Ti is 
824, Ta is 521 and Li is 858, in round numbers, and hence the 
expression for W gives 379 thermal units as the equivalent of the 
work done per lb. of steam. The supply of heat per lb. is 1165 
thermal units. The efficiency is therefore 0*325. Compare this 

with the number 0*368 which represents the value of — ? ; 

1 In finding numerical values of W from this equation the quantity — may be 


conveniently taken from the table in the Appendix. It is the difference between 
the numbers given there under the headings ip, and </>^ (See § 86, below.) 


namely the eflSciency of a reversible cycle completed by adiabatic 
compression as in the engine of § 67. The absence of adiabatic 
compression has in this case reduced the efficiency by nearly 12 per 
cent. This comparison shows what is lost by the partial mis- 
application of heat which results from letting the feed-water come 
into the boiler cold, to be heated by contact with the hot water 
already there, so that the portion of heat represented by Ai — Aj is 
taken in at temperatures lower than the top of the range. 

79. Extension to the oaae of steam not initiallsr drj. 

The result arrived at in the last paragraph may be readily 
extended to cases where the steam is not dry when the adiabatic 
expansion begins. Let qi be the dryness at this stage : then the 
heat taken in during evaporation is qiLi per lb. of working sub- 
stance, but the heat taken in during the heating of the water up 
to Ti remains what it was before. The expression for the work 
done per lb. of feed-water (assuming complete adiabatic expansion 
as before) is therefore found by substituting q^Li for Zj in equa- 
tion (7) or (8), giving, 

F = A,-.A,-T.log.I^ + *M^::^) (9). 

80. Derivation of the adiabatic equation fi*om this 
result. This result may be applied to prove the equation for the 
adiabatic expansion of steam which was stated, without proof, in 
§ 65. The whole heat taken in, per lb., in raising the water from 
any temperature Tj to Tj and in evaporating the fraction qi of it at 
the temperature Ti is 

th — Ih + qiLi. 

By expanding this mixture adiabatically to the temperature r^ 
and then condensing it, we get an amount of work equal (by 
the equation which has just been given) to 

Hence, subtracting the work done from the heat supplied we find 
that the heat rejected is 


But the only rejection of heat in the cycle takes place during the 
E. 7 


condensation at r, after adiabatic expansion, and the amount of 
heat so rejected is 

where q^ is the dryness after adiabatic expansion to the temperature 
Hence 5^, = £:^» + Talog.^ 

?^^^ + log,Il. 


Now T, may be any temperature lower than Ti, for the adiabatic 
expansion might be stopped at any point along the curve and the 
cycle completed by condensing the mixture at the temperature it 
had then reached. Hence this equation serves to show in a 
perfectly general way the change of dryness which takes place 
during adiabatic expansion and, dropping the second suffix, we 
may write it 

?^=?^+iog.l; ..(10), 

which is the same as equation (10) in § 65. It is to be noticed 
that in deriving this expression the specific heat of water has been 
treated as constant. The result is therefore (to a very small 
extent) inexact, especially at high temperatures. 

81. Entropsr. When a substance takes in or rejects heat it 
is said to change its entropy, the change of entropy being de- 
fined by the expression 

each element SQ of the heat taken in or rejected being divided by 
the absolute temperature which the substance had at the time. 
In dealing with entropy, just as in dealing with total heat, it is 
convenient to choose some arbitrary starting-point and reckon the 
entropy fix>m that point as a zero. Thus in reckoning the entropy 
of steam at any temperature we may take the condition of water 


at 32° Fah. as a convenient datum and calculate S — firom that, 


calling the value so calculated the entropy of the steam. Entropy 
will be denoted by ^ : in giving it numerical values it is to be 
reckoned per unit mass of the substance \ 

1 The name Entropy was first used by Glausius. Rankine calls the " Thermo- 
dynamic Fonction." ^ 


It follows from this definition that when any substance is 
going through an adiabatic process its entropy does not change. 
Further we have seen (§ 77) that when a substance is carried 
through a complete reversible cycle 


when the whole cyclic operation is considered. Hence when the 
cycle is complete the entropy of the substance, as well as its 
pressure, temperature, volume and internal energy, has returned 
to the value which it had at the beginning of the cycle. 

Consider now a cycle consisting of two isothermal and two 
adiabatic operations, fig. 20. In 
passing from a to 6 by the \ • 

isothermal line Ti the substance 

gains entropy — , where Qi is the 

heat taken in during this opera- 
tion. Along the adiabatic line 
from 6 to c there is no change 
of entropy. In the isothermal 
line cd the entropy is reduced by 

— , and from dto a there is again ^'®- ^' 

no change of entropy. Now -?^^ = -^ * which means that the entropy 

changes by the same amount whether we pass from one adiabatic 
line ad to another adiabatic line be by one isothermal path ab or 
by any other isothermal path dc. And moreover the change of 
entropy between one adiabatic and another will be the same 
whether the cross-path be isothermal or not, for a curve expressing 
any relation between P and V may be regarded as made up of a 
succession of minute isothermal and adiabatic elements, and 
the change of entropy along such a curve is the sum of the 
changes which occur during the isothermal elements of the process, 

and is still equal to -^ for any single isothermal path between the 

same pair of adiabatic lines. 

We see, then, that not only is there no change of entropy 
during an adiabatic process, but there is a perfectly definite 
change of entropy when a given substance passes from one 




adiabatic line to another, by whatever path. Just as isothermal 
lines are lines of uniform temperature so adiabatic lines are lines of 
uniform entropy, and just as isothermal lines can be distinguished 
by numbers Ti, Ts, etc. denoting the particular temperature for 
which each is drawn, so adiabatic lines can be distinguished by 
numbers ^i, ^j, etc. denoting the particular value of the entropy 
on each. The conception of entropy as that characteristic of a 
substance which does not change during adiabatic expansion or 
compression is of considerable service in problems relating to 
heat-enginea We proceed to show some of the uses to which 
this notion may be put. 

82. Entropsr of Steam : Derivation of the Adiabatic 
Equation. Beckoning from water at any initial temperature Tq 
the entropy of steam (taken wet, for greater generality) 

The first term represents the entropy which is acquired during 
the heating of the water firom Tq to Tj, which is the temperature of 
evaporation, and the second term represents what is acquired 
during evaporation, ji being the dryness of the steam. Treating 
the specific heat of water as unity we can write dr for dh; 
then integrating, 

*=log.T,-log.To + ?^^ (11). 

Now in adiabatic expansion we have 

if} = constant, 

and hence if the steam be expanded adiabatically to any tempera- 
ture T 

log.T^-log,To+^^=log.Ti-log,Ta + ^', 

from which 2^^=Mi + iog.Il, 

which is the adiabatic equation of § 65, already derived by 
another and longer method in § SO- 
BS. Entropy-Temperature Diagrams. The familiar way 
to represent graphicallyv those changes which a working substance 
undergoes in tlie action \of a heat-engiiie is to draw the indicator 
diiagram, which shows pressure in relation to volume. Another 


way is to draw a diagram showing the relation of the temperature 
of the substance to its entropy. Diagrams of this kind form an 
interesting and often useful alternative to the ordinary indicator 
diagram \ Let S^ be the small change in entropy which a sub- 
stance undergoes when it takes in any small quantity BQ of heat 
at any temperature t. By the definition of entropy 








the integration being performed between any assigned limits. 
Now if a curve be drawn with t and ^ for ordinates, /rd^ is the 
area under the curve. This by the above equation is equal to 
JdQ, in other words the area under any portion of the entropy- 
temperature curve is equal to the whole quantity of heat taken in 
while the substance passes through the states which that portion 
of the curve represents. Let ab, 
fig. 21, be any portion of the curve 
of if} and T. The area of the cross- 
matched strip whose breadth is B^ 
and height t, is tB^, which is equal 
to BQ the' heat taken in during the 
small change B<t>. The whole area 
mabn or /rd^ between the limits a 
and b is the whole heat taken in 
while the substance changes fi:om 
the state represented by a to the 
state represented by b. Similarly, in 
changing trom state b to state a by the line ba the substance 
rejects an amount of heat which is measured by the area bamn. 
The base line ox corresponds to the absolute zero of temperature. 

When an entropy-temperature curve is drawn for a complete 
cycle of changes it forms a closed figure, since the substance 

Entropy * 

Fio. 21. Entropy-Temperature 

1 Entropy-Temperature diagrams were first described along with other graphic 
methods in thermodynamics by Professor J. Willard Gibbs (Trant, of the Con- 
necticut Acad, of Sciences^ Vol. ii. 1873, p. 309). Their application to steam-engine 
problems is mainly due to Mr J. Macfarlane Gray (see Proc. Inst* MecK Eng. 1889, 
p. 399). 


returns to its initial state. To find the area of the figure we have 
to integrate throughout the complete cycle, when 

Qi being the heat taken in and Q3 the heat rejected. But the 
difference between these is the heat converted into work, hence 

Jrd<f> = W (13), 

when the integration extends round a complete cycle and W is 
expressed in thermal units. Thus entropy-temperature diagrams 
have the important property in common with pressure-volume 
diagrams that the enclosed area measures the work done in a 
complete cycle. 

Isothermal lines on an entropy-temperature diagram are straight 
lines parallel to oa? whatever be the 
working substance : adiabatic lines are 
straight lines parallel to oy, being lines 
of constant entropy. Hence Camot's 
cycle whether with air or steam or any 
other substance would be represented | 
by a rectangle abed, Fig. 22, in which "^ 
the heat received 

Qi = area aJbnm s= Ti (^ — <l>'), 

Q Entropy 

heat rejected ^^^ ^ ^^^^.^ ^^^ ^^ 

Q, = area cdmn = t, (^ - <f>') ^? Entropy-Temperature 

and work done 

W = area abed = (tj — Tj) (^ — <f>'), 

if) being the entropy in the adiabatic process of expansion and (f/ 
the entropy in the adiabatic process of compression. The effici- 
ency is 

area abed _ Ti — Tg 

area abmn "" tj 

84 Entropy-Temperature Diagram fbr Steam: appli- 
cation to ideal steam-engine working without compressioA 
but with complete expansion. A more interesting example 
of the use of temperature-entropy diagrams is given by the 
engine of § 71, where after complete adiabatic expansion from 
Tj to Ta the steam is condensed isothermally at Tj, and is then 
returned as water to the boiler. In drawing the diagram for this 


cycle we shall begin at the point where the water, at t„ is about to 
be heated Reckoning &om some standard (lower) temperature Tq 
and dealing throughout with 1 lb. of the working fluid, we have 

Entropy of water at any temperature t = I — « I , 

where <r is the specific heat of water. The specific heat is equal 
to unity at low temperatures and becomes only a very little more 
than unity at high temperatures. Neglecting this small change, 
we may write 

Entropy of water = / — = log, t — log, To, 

Jr. '^ 

which relates to any stage in the heating of the feed-water from t, 
to Ti. The first part of the diagram is therefore a logarithmic 
curve, oft, fig. 23, where Ta = Ta, Tft = Ti, <^a = log,Ta-log,To, and 
(fn, = log, Ti — log. To. Hence <t>b — <^a or mn = log, Ti — log, Tj. It is 
a matter of indifference, in the drawing of the diagram, at what 
distance the origin is taken to the lefb of m ; in other words, what 


e r^'Se2 



Fio. 23. Entropy-Temperatnre Diagram for Steam. 

value of To is taken as a datum in reckoning the entropy. In the 
example sketched in the figure the entropy of water at 32"^ Fah. is 
reckoned to be zero: r^ is taken to be 662 and r^ to be 834; 
Ta therefore corresponds to a steam pressure of 1 lb. per square 
inch and r» to a pressure of 180 lbs. per sq. inch. At h steam 
begins to be formed, and 6c is the change of entropy which the 



8ubBtanoe undergoes in passing from water to steam at the con- 
stant temperature Ti. bo is therefore equal to — , assuming the 

,poration to be complete. I If incomplete, be = ^-^ . j The adia- 

batic process of complete expansion down to the temperature Ts is 
represented by cd, and da is the process of condensation which 
completes the cycle. 

The heat taken in during the warming of the feed-water is 
the area maAn. The heat taken in during evaporation is nbcp. 
The work done is the enclosed area abcda. The heat rejected is 
pdam. Of the heat taken in during the process of evaporation, 
namely the area bp, the part measured by the area bd is converted 

into work : it represents the fraction ^ or — of the whole, as 

we should expect. Of the heat taken in during the process of 
warming the feed-water a smaller fraction is converted into heat, 

namely the fraction — r- . This is because the heat is less advan- 

tageously supplied during this operation, the temperature being 
then less than r^. An engine going through Camot's cycle would 
have the diagram ebcd. The present engine does more work (by 
the area (ibe\ but to do this it has to take in a more than propor- 
tionally larger amount of heat and is therefore less efficient. It 
will be seen that the diagram exhibits in a very simple way results 
which we have already arrived at by other routes. 

Further, let a curve cf be drawn such that the distance from 
any point in ab to it, measured horizontally (that is, parallel to 

op), is equal to the value of — corresponding to that point Thus 

let o^be equal to ~ , / being the point where ad produced meets 

this curve. Then the dryness of the steam after the process of 
adiabatic expansion represented by cd is given by the fraction 

-7; . This follows from the fact that if the steam were perfectly 

dry at r^ the heat given out during its condensation would be equal 
to the area qfam, whereas the heat actually given out is equal to 
pdam. In other words, the former area is Z, and the latter is 
9ȣs, q^ being the dryness when the stage d is reached, whence 



jj = — >. In the same way a straight line drawn horizontally 
from any point % in cd (fig. 24) to meet the curves cf and ab is 


-s — y 

Fio. 24. 

divided by cd into segments il and ik. These are proportional to 
the quantities of steam and water respectively which make up the 
working substance when the expansion has advanced as far as the 

point i. In other words the dryness ?=77. The temperature- 
entropy diagram thus affords a convenient method of finding q 
graphically at any stage in adiabatic expansion. 

Further, suppose the steam has not been dry when adiabatic 
expansion begins. . This state of things is represented on the 
diagram by making the horizontal line from b terminate at a 

point g such that bg = — — : in other words j^ = q^, gh now repre- 
sents the process of adiabatic expansion and the construction just 
described is still applicable to find q at any stage. Thus at h, 

5 = -^; -=4 is the proportion then present as water. 

Again, reverting to the Camot cycle of fig. 14, § 67, we can 
use the entropy-temperature diagram to determine the point at 
which condensation at Tj must be stopped in that cycle in order 
that adiabatic compression may bring the substance to the state 
of water at Tj. The process of compression required for this is eb 
(fig. 23 or 24), and hence the process must begin when the pro- 

portion of steam still uncondensed is ^, Similarly the fraction 


^ measures the dryness at any stagey* of this adiabatic compression. 


86. Application of the entropy-temperature diagram to 
the case of superheated steam. The entropy of steam super- 
heated to any temperature r is to be found by adding to the 
expression for the entropy in the saturated state the term 


where k is the specific heat of the steam during superheating, that 
is to say, the amount of heat required to raise 1 lb. of the steam l"" 
Fah. when its temperature exceeds Ti the temperature of satura- 
tion. In the absence of more definite knowledge of what happens 
during superheating we may take /e to be roughly constant and 
equal to 0*48 when the process of superheating is performed at 
constant pressure, — ^a condition which applies, for instance, when 
steam is superheated by passing through a coil of pipe in a hot 
flue or furnace on its way from the boiler to the engine. The 
addition to the entropy may then be written 

0-48 f— = 0-48 (log. t'- log. Ti). 
This allows the entropy-temperature line to be extended as in fig. 25, 



/ - 


« d 
♦ p 

Fio. 25. 

where cr is drawn to show the increased amount of entropy produced 
by superheating as calculated for a series of values of r'. After 
superheating to any extent let the cycle be completed by the 
processes rs and sa, namely by adiabatic expansion to temperature 
Ts and condensation at that temperature. The diagram shows 


that^ in consequence of superheating, the work done by the substance 
is increased by the area dcrs while the heat taken in is increased 
by pcru. The eflBciency is slightly increased, since this additional 
heat is received at temperatures somewhat higher than the other 
portions of the heat-supply. But unless superheating be carried 
very far the extra supply of heat is too small a part of the whole 
to make any large difference in the efficiency of the ideal engine 
we are dealing with here. In the case sketched in fig. 25 the 
steam is supposed to be superheated as much as 200"* above the 
boiler temperature, but the diagram shows that even this makes 
but little improvement in the ideal efficiency. In real engines 
superheating does make a marked difference, but its influence is 
indirect and proceeds &om the fact that it tends to prevent 
the steam firom being condensed by contact with the metal of the 
cylinder and piston. This influence will be considered in the 
next chapter. Nothing of the kind takes place in the ideal case 
now dealt with, because here we postulate adiabatic expansion, or, 
in other words, a perfectly non-conducting cylinder and piston. 

It would evidently be fallacious to suppose that when super- 
heating is applied to the steam of the ideal engine the increased 
range of temperature implies anything like a corresponding gain 
of efficiency, for the chief part of the heat is still taken in at the 
temperature of saturation, and its value for conversion into work 
depends on the temperature at which it is taken in, not upon the 
temperature to which the working substance is subsequently 

In the diagram, fig. 25, the adiabatic line rs shows by its 
intersection of the curve cfsktt the stage in the expansion at which 
the steam will cease to be superheated. At this point ^ it is dry 
and saturated : as the expansion proceeds it becomes wet, and at 

the end of expansion the condensed part is ^of the whole. The 

extent to which superheating has to be carried if the steam is 
just to be dry, and no more, at the end of expansion, is readily 
found by drawing a vertical line through / to meet the continuation 
of the curve cr. 

86. Values of the Entropy of Water and Steam. In 

applying this useful graphic method to the investigation of par- 
ticular cases in the expansion of steam it is convenient to have an 


entropy-temperature curve for water and steam drawn on section- 
paper throughout the range of pressures that occur in practice : 
the construction for particular cases is then readily made by 
adding horizontal straight lines to correspond with the formation 
and condensation of the steam, while any adiabatic process is 
represented by a vertical line. 

Such a diagram, carefully drawn to scale, is shown in fig. 26. 
The curves extend throughout the whole range of Table I. and 
more than cover the useful range of pressure. The curve on the 
left marked "water" shows the relation of entropy to temperature 
before steam begins to form: the curve on the right marked 
" steam " shows the same relation when all the water is converted 
into steam. The horizontal distance between the two curves at 
any point, or ^, — ^, represents the gain of entropy which occurs 

while the water is changing into steam (namely —j . An exten- 








— ^ 







— ■ 












2 720 




«B 700 

















1 ' 



2 rvo 





1 «' 







0) 9^Q 


< «9n 















1 d 


2 fl 



B 6 

h 6 

7 6" 









K 1 

I I 





Fio. 26. Entropy of Water and Steam. 

sion of the diagram to the left might be drawn, in the form of 
a horizontal line at 32° Fah. to show the change of entropy when 


ice melts; but this would have no application to our present 
purpose. The numerical values of the entropy relate to 1 lb. of 
water or steam and are reckoned from water at 32"" Fah. In 
calculating the entropy of water allowance has been made for 
the increased specific heat of water at high temperatures. The 
diagram has been drawn by calculating the entropy of water (^w) 
and of steam (</>,) for certain of the points in Table I., from the 
data furnished by Begnault's experiments; the values so calculated 
are given in Table II. below. A more extended table showing 
the entropy of water and steam at various pressures will be founds 
along with other properties of steam, in the Appendix. 

Tablk n. ErUropy of Water and Steam. 



lbs. per sq. in. 






























































From this diagram and fi*om the knowledge of the relation of 
pressure to volume in saturated steam which is furnished by the 
table in the Appendix, it is easy to determine what proportion of 
water will be present at any stage in adiabatic expansion or 
compression, and hence to draw the ordinary indicator diagram or 
pressure-volume curve for an adiabatic process. Thus let BCD, 
fig. 27, be a portion of the pressure-volume curve for saturated 
steam. To draw the adiabatic curve from any assigned point B, 
refer to the table to find the temperature which corresponds to the 
assigned pressure at B, and draw a horizontal line ob at that 
temperature in the entropy diagram (fig. 26). If the steam is 
assumed to be dry at B, draw a vertical line W through b. 
Taking any lower pressure draw the horizontal line NC in the 


pressure-volume diagram (fig. 27), refer to the table for the corre- 
sponding temperature, and then draw the liaepc for that tempera- 
ture in fig. 26. Measure the ratio ^ . This is the dryness at C. 

• 10 12 14 16 IB 


Fio. 27. 

Take a point C in NG (fig. 27) such that ^ '"^^ • Then C is 

(sensibly) a point on the adiabatie curve. The same construction is 
to be repeated to find as many points as are sufficient to let the 
curve be drawn. If the steam is wet to begin with, the initial volume 
of 1 lb. will have some value ME less than MB and the curve of 
adiabatie expansion starts from E. It is found in that case by 

taking e in fig. 26 so that -v = ^^ (the initial dryness), drawing 

the vertical ec'\ and taking C" in fig. 27 so that -^^ =2i_ ^ this 

ratio being the dryness after adiabatie expansion has brought the 
pressure of the mixture down to the level of pressure NC; (7" is 
then a point in the required curve. The curve EG^^D" has been 
sketched in this way to show the adiabatie expansion of steam 
containing 25 per cent, of moisture to begin with. 

In the example sketched the pressure at M is 70 lbs. per 
square inch, and at N it is 25 lbs. per square inch. The lines ob 
and pc are drawn in fig. 26 at the corresponding levels of tempera- 

Not the least merit of the entropy-temperature diagram as a 
means of representing graphically the cycle of operations in a 


heat-engine is that it shows the heat taken in and the heat 
rejected, as well as the work done, and so allows estimates of 
efficiency to be made by inspection of the diagram itself. The 
advantage, for instance, which results from raising the initial 
pressure of the steam is readily shown in a diagram such as fig. 23 
by drawing horizontal lines at temperatures corresponding to the 
initial pressures which are to be compared, and vertical lines 
through the points where they meet the entropy curve of satu- 
rated steam (c/*), the vertical lines being continued to meet the 
base, which is the absolute zero of temperature. Comparison of 
the enclosed areas then shows that while the heat taken in is but 
slightly increased with higher boiler pressure there is a more 
considerable gain of work, a result which is of course to be 
expected from the fact that the general temperature of reception 
of the heat is raised. 

If a vertical line such as ed' in fig. 26 be drawn to represent 
the adiabatic expansion of a mixture of steam and water, it is 
clear fix)m the diagram that when e is chosen at less than a certain 
distance from o, that is to say, when there is a certain degree of 
initial wetness, the mixture will become drier as it begins to 
expand, instead of wetter as is the case when the initial proportion 
of water is less. In the region of ordinary working pressures the 
" water " and " steam " curves of fig. 26 have nearly equal inclina- 
tions to the vertical line which represents an adiabatic process. 
Hence if such a line be drawn starting from a point midway 
between the two curves it will continue to lie nearly midway 
between them : in other words if there is about 50 per cent, of 
water present at the beginning of adiabatic expansion, nearly the 
same percentage will be found as the expansion goes on. When 
the steam is much wetter than this to begin with, adiabatic 
expansion makes it drier. 

It will be shown later that the entropy-temperature diagram 
is also of service in exhibiting the changes of dryness which occur 
in real steam-engines, where the action is by no means adiabatia 

87. Entropy-temperature diagram for Steam used non- 
eaq;ianiiyely. By way of contrast with the cases treated in 
§§ 83 and 84, we may draw the entropy-temperature diagram for 
a steam-engine working without expansion. The four steps of the 
cycle have been stated in § 69, and the volume-pressure diagram 


is drawn there (fig. 15). In the entropy-temperature diagram 
(fig. 28) we have the four corresponding lines ab,bc,cd,da. a& is 
the heating of the water from Ts to Ti. &c is the conversion of the' 

-^ '-^ — V 

Fio. 28. Entropy-temperature diagram of steam need non-expansively. 

water into steam, cd the partial condensation which takes place 
when the cold body is applied, the piston meanwhile remaining at 
the end of its forward stroke, and da is the remainder of the 
condensation, which occurs while the piston is pressed in, the cold 
body being still applied, cd is a Une of constant volume, for 
throughout the change which it represents the substance remains 
in the cylinder and there is no movement of the piston. To find 
points in cd, draw the saturation curve c/* as in former examples 
and at any temperature t intermediate between Ti and t, draw the 

line Ik We have to divide Ik in a point e such that jj- shall 

represent q, the dryness of the steam at the time its temperature 
has fallen to t. The dryness q is determined by the consideration 
that qVis sensibly equal to Vi, where Fis the volume of 1 lb. of 
saturated steam at t and Vi is the volume originally occupied by 
1 lb. before the process of condensation began. Throughout the 
operation cd the volume of the substance remains unchanged and 

equal to Vi, Hence $ = -w , and e is found by making 


The work which is lost through the absence of adiabatic 
expansion is the area cgd. In the example sketched the initial 
pressure is 180 lbs. per sq. inch, and the pressure during the 
return stroke da or the '* back-pressure" is 3 lbs. per square inch. 
In other words Ti is taken as 834 and Ts as 603. 

^ 88. Incomplete ezpaniion. The case of incomplete expan- 
sion admits of similar treatment. Let adiabatic expansion be 
carried on until, at the end of the stroke, the temperature has 


fallen to the level indicated by d in the entropy-temperature 
diagram, fig, 29. This process is represented by the line cd^ 
Then let the steam be suddenly cooled by applying the cold body. 
The constant- volume curve dd shows this cooling; after which the 
return stroke takes place, which is shown by da. To draw the 
curve dd take e at any level, such that 

where Y' is the volume of 1 lb. of saturated steam at the tempera- 
ture corresponding to c', and y' is the dryness at c', which is equal 

^ mo' 
to - — . 

Fio, 29. Entropy-temperature diagram showing incomplete expansion of steam. 

In the example sketched in fig. 29 the pressure is reduced by 
adiabatic expansion in the operation cd from 180 to 20 lbs. per 
square inch, and the back pressure is 3 lbs. per square inch as in 
fig. 28. 

In dealing with the process of sudden condensation represented 
by the line cd in fig. 28 and cd in fig. 29 we have supposed, to 
simplify the statement, that the steam is retained in the cylinder 
and the cold body is applied to it. But it makes no difference if 
the steam be allowed to escape into a separate vessel, to be 
condensed there. Just the same amount of work is done, for the 
pressure on the piston is the same in that case as in the other. 
Hence the area of the entropy-temperature diagram is unaffected, 
and since that is true whatever be the value of t, the form of the 
curve cd or dd is unchanged^. 

1 The constant-Tolnme oarve cd or e'd in the entropy-temperatnre diagram, 
may he more conveniently drawn as follows by an application of equation (3) of § 75. 
Let V represent the volome of the mixture of steam and water at any stage in the 
process of condensation, the temperature then being r. Let X represent the heat 
which would be given out if the condensation of the mixture were completed at th& 
temperature r. Then by that equation 

JX dr 




B9. EnlTopy-temperature diagrams in engines using a 
Regenerator. An engine such as Stir- • • 

ling's which substitutes the use of a 
regenerator for the adiabatic expansion 
and compression in Camot's cycle has a 
diagram of the type shown in fig. 30. 
The isothermal operation of taking in 
heat at Ti is represented by ah ; be is the 
cooling of the substance from Ti to. Tj in 
its passage through the regenerator, when 
it deposits heat: cd is the isothermal 
rejection of heat at Tj; and da is the 
restoration of heat by the regenerator 
while the substance passes through it 
in the opposite direction, by which the 
temperature is raised from t, to t^. Assuming the action of the 
regenerator to be ideally perfect, be and ad are precisely similar 
curves whatever be their form. The area of the figure is then 
equal to the area of the rectangle which would represent the 
ordinary Camot cycle (fig. 22). The equal areas pbcq and ndam 
measure the heat stored and restored by the regenerator. 

When the working substance is air and the regenerative 
changes take place either under constant volume, as in Stirling's 
engine, or under constant pressure, as in Ericsson's, so that the 

Fio. 30. Entropy-tempera- 
ture diagram of perfect 
engine using a Begene- 

10 being the volume when the substance is all water. Hence 


U-w dP 
J dr' 


But - is the length le, if the line le be drawn at the level r, and U is the volume of 
the cylinder, which is constant. We therefore have 

a relation which allows le at any level of temperature to be readily determined when 
the values of -^ for saturated steam are known. These may be found by measure- 
ment of the slope of the pressure-temperature curve, or approximately from the 
-table of P and r in the Appendix by dividing small differences of pressure by 
•corresponding differences of temperature. 

The method of drawing cd described in the text is given by Professor Cotterill 
in the second edition of his Treatise on the Steam^Engine, p. 802. The examples 
sketched here (fig. 2S and 29) are drawn to scale. 


specific heat K is constant^ ad and he are logarithmic curves with 
the equation 

<^ = j -;j^ = iriog.T, 
K being K^ in one case and Kp in the other. 

90. Joule'8 Air-Engine. A type of air-engine was pro- 
posed by Joule which, for several reasons, possesses much interest. 
Imagine a chamber G (fig. 31) full of air (temperature r,), which is 

Fia. 81. Joule's proposed Air-Engine. 

kept cold by circulating water or otherwise; another chamber 
A heated by a furnace and full of hot air in a state of compression 
(temperature Tj) ; a compressing cylinder M by which air may be 
pumped from G into A, and a working cylinder N in which air 
from A may be allowed to expand before passing back into the 
cold chamber G, We shall suppose the chambers A and G to be 
large, in comparison with the volume of air that passes in each 
stroke, so that the pressure in each of them may be taken as 
sensibly constant. The pump M takes in air from (7, compresses 
it adiabatically until its pressure becomes equal to the pressure in 
A, and then, the valve v being opened, delivers it into A. The 
indicator diagram for this action on the part of the pump is the 
diagram /doe in fig. 32. While this is going on, the same quantity 
of hot air from A is admitted to the cylinder Ny the valve u is then 
closed, and the air is allowed to expand adiabatically in N until 
its pressure falls to the pressure in the cold chamber G. During 



the back stroke of N this air is discharged into C. The operation 
of N is shown by the indicator diagram ebcf in fig. 32. The area 

Fia. 32. Indicator diagram in Joule's Air-Engine. 

fdde measures the work spent in driving the pump ; the area ebcf 
is the work done by the air in the working cylinder N. The 
difference, namely the area abed, is the net amount of work 
obtained by carrying the given quantity of air through a complete 
cycle. Heat is taken in when the air has its temperature raised 
on entering the hot chamber A, Since this happens at a pressure 
which is sensibly constant, 

where tj is Ti, the temperature of A, and t^ is the temperature 
reached by adiabatic compression in the pump. Similarly, the 
heat rejected 

where t<i = t„ the temperature of (7, and Tc is the temperature 
reached by adiabatic expansion in N. Since the expansion and 
compression both take place between the same terminal pressures, 
the ratio of expansion and compression is the same. Calling it r, 
we have 



md hence also 






I? = 

and the 






i T 





This is less than the efficiency of a perfect engine working 
between the same limits of temperature f-^^ -j because the heat 

is not taken in and rejected at the extreme temperatures. 

Instead of having a cold chamber, with circulating water to 
absorb the rejected heat, the engine may draw a fresh supply at 
each stroke from the atmosphere and discharge into the atmosphere 
the air which has been expanded adiabatically in N. 

The entropy-temperature diagram for this cycle is drawn 
in fig. 33, where the letters refer to the same 
stages as in fig. 32. After adiabatic compression 
da, the air is heated in the hot chamber A 
and the curve ab for this process has the 

'^=r^ = ^pOog.r-log.T.). 

Jr. T 

Then adiabatic expansion gives the line be, 
and cd is another logarithmic curve for the re- 
jection of heat to C by cooling under constant 

pressure. The ratio ^ which is represented by j,J" 33 ^^^^. 

temperature dia- 
g in fig. 32 and by ^ in fig. 33. shows the K^^ef"'^'' 

proportion which the volume of the pump M must bear to the 
volume of the working cylinder N. The need of a large pump 
would be a serious drawback in practice, for it would not only 
make the engine bulky but would cause a relatively large part of 
the net indicated work to be expended in overcoming friction 
within the engine itself 

In the original conception of this engine by Joule it was 
intended that the heat should reach the working air through the 
walls of the hot chamber, from an external source. But instead 
of this we may have combustion of fuel going on within the hot 
chamber itself, the combustion being kept up by the supply of 
fresh air which comes in through the compressing pump, and, of 
course, by supplying fuel either in a solid form from time to time 
through a hopper, or in a gaseous or liquid form. In other words, 
the engine may take the form of an internal cornbustUm engine. 
Internal combustion engines^ essentially of the Joule type, employ- 
ing solid fuel have been used on a small scale, but by far the 


most important development of this type is the explosive gas- 
engine. Its cycle is substantially Joule's, considerably modified, 
however, by features which will be noticed in a later chapter. 

This, however, is not the only reason why Joule's cycle is now 
interesting. In modern practice it has found application in the 
reversed form. The refrigerating machines which are used to 
keep the temperature of rooms on board ship below the freezing 
point, to allow frozen meat to be carried over seas, work, as we 
shall see immediately, by reversing the cycle suggested by Joule. 

91. Re^enal of the cycle in heat-enginee : Refrige- 
rating Machines or Heat-Pumpe. By a refrigerating machine 
or heat-pump is meant a machine which will carry heat from a 
cold to a hotter body. This, as the second law of thermo-dynamics 
asserts, cannot be done by a self-acting process, but it C€ui be done 
by the expenditure of mechanical work. Any heat-engine will 
serve as a heat-pump if it be forced to trace its indicator diagram 
backwards, so that the area of the diagram represents work spent 
on, instead of done by, the working substance. Heat is then taken 
in from the cold body and heat is rejected to the hot body. 

Take for instance the Camot cycle, using air as working 
substance (fig. 34), and let the cycle 
be performed in the order dcba, so 
that the area of the diagram is nega- 
tive, and represents work spent upon 
the machine. In stage dc, which is iso- 
thermal expansion in contact with the 
cold body C, the gas takes in a quan- 
tity of heat from C equal to era log, r 
(§ 40), and in stage ba it gives out 
to the hotter body A a quantity of 
heat equal to ctj log, r. There is no Fio. 34. 

transfer of beat in stages cb and ad. 

Thus (7, the cold body, is constantly being drawn upon for heat 
and can therefore be maintained at a temperature lower than its 
surroundings. In an actual refrigerating machine used for making 
ice, C consists of a coil of pipe through which brine circulates 
while the working air is brought into contact with the outside of 
the pipe. The brine is kept by the action of the machine at a 
temperature below 32"* F. and is used, in its turn, to extract heat 


by couduction from the water which is to be frozen. The " cooler " 
A, which is the relatively hot body, is kept at as low a temperature 
as possible by means of circulating water, which absorbs the heat 
rejected to A by the working air. 

The use of a regenerator, as in Stirling's engine, may be 
resorted to in place of the two adiabatic stages in this cycle, and 
this has the advantage of making the machine much less bulky. 
Refrigerating machines of this kind using air as working substance, 
with a regenerator, were introduced by Dr ^. C. Bjrk and have 
been widely used^ The working air is completely enclosed, which 
allows it to be in a compressed state throughout, so that even 
its lowest pressure is much above that of the atmosphere. This 
makes a greater mass of air pass through the cycle in each 
revolution of the machine, and hence increases the performance of 
a machine of given size. 

In another class of refrigerating machines the working sub- 
stance, instead of being air, consists of a liquid and its vapour, 
and the action proceeds by alternate evaporation under a low 
pressure and condensation under a 'relatively high pressure. A 
liquid must be chosen which evaporates at the lower extreme 
of temperature under a pressure which is not so low as to 
make the bulk of the engine excessive. Ammonia, ether, sul- 
phurous acid and other volatile liquids have been used. Ether 
machines are inconveniently bulky and cannot be used to produce 
intense cold, for the pressure of that vapour is only about 1*3 lbs. 
per square inch at 4"^ F. and to make it evaporate at any tempera- 
ture nearly as low as this would require the cylinder to be exces- 
sively large in proportion to the performance. This would not 
only make the machine clumsy and costly but would involve 
much waste of power in mechanical friction. The tendency of 
the air outside to leak into the machine is another practical 
objection to the use of so low a pressure. With ammonia a 
distinctly lower limit of temperature is practicable : the pressures 
are rather high and the apparatus is compact. 

Engines of this type are usually arranged to act as follows, in 
a cycle which is nearly but not quite the reverse of Camot's. 

1 See Kirk, On the Mechanical Production of Cold, Min, Proc, Inst, (7. E. Vol. 
xzzvn., 1874. Also Lectures on Heat and its Mechanical Applications, Inst. C, E. 


The organs, which are shown diagrammatically in fig. 35, are (1) a 
compressing cylinder, (2) a cold body C which serves as boiler for 
the volatile working fluid and allows heat to pass into the working 
fluid from the water or other substance that is to be made cold, 
and (3) a cooler A such as a coil of pipe surrounded by circulating 
water, in which the working fluid is condensed under pressure. 
The steps of the cycle are shown by the indicator diagram in the 

Fio. 85. Refrigerating Maehine adng the vapour of a liquid. 

same figure ; dc is the forward stroke, during which the cylinder 
is taking in vapour from G at the uniform pressure corresponding 
to the lower limit of temperature Tj. 

ch is the first part of the back stroke. The valves leading to 
both chambers are shut. This continues till the pressure in the 
cylinder becomes equal to the pressure in A. 

Next, the communication with A is opened and the back 
stroke is completed, the working substance passing into A and 
being condensed there (6a). 

To complete the cycle, the valve v is opened till the same 
quantity of the substance passes directly from A\^ C (ad). 

This last step in the process is not reversible, but it is a simpler 
way of completing the cycle than to complete it reversibly by 
letting the fluid do work in an expansion cylinder in passing from 
A to C, and the amount of work that would be saved if that were 
done is inconsiderable. 


92. Coefficient of Performance of Refrigerating 
Machines. The ratio 

Heat extracted from the cold body 
Work expended 

may be taken as a coeflBcient of performance in estimating the 
merit of a refrigerating machine from the thermodynamic point of 
view. When the limits of temperature Ti and Tj are assigned it is 
easy to show by a slight variation of the argument used in § 45 
that no refrigerating machine can have a higher coefficient of 
performance than one which is reversible in Carnot's sense. For 
let a refrigerating machine S be driven by another R which is 
reversible and is used as a heat-engine in driving S. Then if S 
had a higher coefficient of performance than R it would take from 
the cold body more heat than R (working reversed) rejects to the 
cold body, and hence the double machine, though purely self- 
acting, would go on extracting heat from the cold body in violation 
of the Second Law. Keversibility, then, is the test of perfection 
in a refrigerating machine just as it is in a heat-engine. 

When a reversible refrigerating machine takes in all its heat, 

namely Q^ at Tj and rejects all, namely Q^, at Ti, -- = — and the 

Ta Ti 

coefficient of performance 

Hence — and the inference is highly important in practice — the 
smaller the range of temperature is the better. To cool a large mass 
of any substance through a few degrees will require much less ex- 
penditure of energy than to cool one-tenth of the mass through ten 
times as many degrees, though the amount of heat extracted is the 
same in both cases. If we wish to cool a large quantity, say of water 
or of air, it is better to do it by the direct action of a refrigerating 
engine working through the desired range of temperature, than to 
cool a portion through a wider range and then let this mix with 
the rest. This is only another instance of a wide general principle, 
of which we have had examples before, that any mixture or contact 
of substances at different temperatures is thermodynamically waste- 
ful because the interchange of heat between them is irreversible. 
An ice-making machine, for example, should have for its lower 
limit a temperature only so much lower than 32'' F. as will allow 


heat to be conducted with sufficient rapidity from the water that 
is to be frozen to the working fluid. 

93. Reversed Joule Eng^e: the Bell-Coleman re- 
frigerating machine. This machine was briefly mentioned in 
§ 89 as the one now largely employed to cool the air in the frozen- 
meat chambers of ocean steamships. It acts by drawing in a 
small portion of the atmosphere of the chamber, compressing that 
and extracting as far as possible by means of a cooler the heat 
developed by compression, then expanding the air until its pres- 
sure falls to that of the chamber. Its temperature is then lower 
than the temperature of the chamber in consequence of the 
removal of heat which took place while it was compressed. The 
air thus chilled by expansion is then returned to the chamber, 
and in this way the temperature of the chamber is kept down 
notwithstanding the heat which reaches it by conduction from 
outside. The chamber has a thick lining of poorly conducting 
matter in order to reduce as far as may be the work which has to 
be spent on refrigeration. 

The sketch, fig. 36, shows the organs diagrammatically. C is 

Coder A 
Fio. 86. Organs of the Bell-Coleman Befrigerating Machine. 

part of the cold chamber, which is at or about atmospheric pres- 
sure, and A is the cooler, a set of pipes with circulating water. 
Compression takes place in M and expansion in i\r. M takes in 
air from C at temperature r, during its out-stroke, and compresses 
that during part of its in-stroke till the pressure becomes equal to 
the pressure, in A, These two operations are represented by the 


lines /c and cb in the indicator diagram, fig. 37. The compressioD 
06 has the effect of raising the temperature of the air above that 
of A. Consequently when the pump delivers the compressed air 
into A, by completing its return stroke (bc\ which is the next 
operation, the temperature of the air falls and a quantity of heat 
is rejected to A, namely 

where tj is the temperature reached by compressing, and Ta is Ti 

Fig. 37. 

the temperature of A. While this is going on, the cylinder N 
takes an equal quantity of air from A at Ti or Ta, and expands it 
to the pressure of C: these operations are shown by the lines ea 
and ad in the indicator diagram. At the end of this expansion 
the temperature t^ is lower than that of the cold chamber. 
Finally the chilled air is discharged into C during the return 
stroke of N, which is shown by the line df in the indicator 
diagram. The net amount of work expended is badc,fcbe being 
the indicator diagram of work spent upon the pump M and eadf 
being the diagram of work recovered in the expansion cylinder N. 
The net amount of heat taken from the cold chamber is Kp (t<. — t^). 
Assuming the processes cb and ad io he adiabatic, the ratio of 
expansion in N is equal to the ratio of compression in M and 

hence -^ = — , as we have already seen in treating of the Joule 
cycle (§ 90) of which this is simply a reversal. Also ^ = ~ and 
the coeflScient of performance ^ ^^ — — — 
— - — for the same reason that Joule's engine is less efficient than 



- , a value less than 


In practice the compression in JIf is not adiabatic : by using a 
water-jacket, or by injecting water into the cylinder itself, the 
compression is made to follow a curve which lies between an 
adiabatic and an isothermal line. This has the thermodynamic 
advantage that some heat is extracted at a lower temperature 
than would be the case if compression were completed before the 
action of the cooler began. Or, to take another point of view, the 
net expenditure of work is reduced, since the compression curve 
from c rises less steeply than the adiabatic line cb, 

A difficulty attending the use of machines of this type arises 
from the fact that the working substance is not dry air. It 
contains water-vapour in solution, as all air does except when 
specially dried, and when the temperature falls this tends to be 
condensed and even frozen. Provision has therefore to be made 
against the clogging of valves and passages by snow or hoar-frost 
deposited by the working air. This difficulty is of course aggra- 
vated when injection water is used to cool the air during compres- 
sion. In Mr Lightfoot's form of the machine the expansion is 
performed in two stages ; there is a compound pair of expansion 
cylinders in the first of which the temperature of the air is 
reduced to only about 35° F. At this temperature the greater 
part of the water- vapour is deposited, as water, which is drained 
away, and the air then goes on to the second cylinder where it 
completes its expansion. In Mr Coleman's own form of the 
machine the compressed air after giving up heat through tubes to 
water in the ordinary cooler, is further cooled by passing through 
pipes which are exposed to the action of chilled air from the 
chamber, and is thus forced to give up its suspended moisture 
before it is allowed to expand*. 

94. The Reverted Heat-Engine as a Wanning Ma- 
chine. It was pointed out by Lord Kelvin in 1852 that the 
reversed heat-engine cycle might serve not only as a means of 
cooling but as a means of warming". Let it be required for 
instance to raise and keep the temperature of a room above the 

^ For particulars of the oonstmotion and performance of these machines see 
Coleman, Min, Proe, Inst. C. E. Vol. Lzvni., 1882, p. 146; Lightfoot, Proe, Imt, 
Mech, Eng, 1881, p. 105 ; also the papers of Dr Kirk referred to above. 

2 Proc, of the Phil, Soc. of QUugow, Vol. ni. p. 269, or CoUeeted Papert^ Vol. i. 
p. 515. 


temperature of the surrounding air. A machine resembling the 
Bell-Coleman t3rpe may take in air at atmospheric temperature, and 
compress it, thus raising its temperature. The air so warmed can 
be made to give up its heat to the room by direct conduction (say 
by being sent through pipes placed in the room) or by heating 
water which in turn heats the room. Then let the working air 
be expanded till its pressure falls to that of the atmosphere, into 
which it is discharged. The effect is, that by expending some 
mechanical work a quantity of heat is transferred from the cold 
atmosphere to the warmer room, — a quantity which may be tar 
greater than the thermal equivalent of the work spent in driving 
the machine. For if the machine were reversible the heat rejected 
to the room A, namely Q^, would be to the heat extracted from 
the atmosphere, namely Qc, as Ti is to Ta, and 
Qa^ Qa ^ r, 

where W is the work expended, expressed in thermal units. 
When the range of temperature is small Q^ may be many times 
greater than TT, that is to say a very large amoimt of heating 
through a small range may be achieved with but little expenditure 
of mechanical work. 

The importance of the suggestion lies in the fact that the neces- 
sary power may be obtained, by means of a heat-engine, with a 
smaller supply of heat than would be required to effect the warming 
directly, provided the range of temperature of the warming be less 
than the range through which the heat-engine works in generating 
the required power. Burning fuel to warm a room by a few 
degrees is a wasteful way to utilise heat, even if all the heat of 
combustion be conceived to pass into the air of the room. The 
high-temperature heat produced in the combustion of coal or gas 
could warm a much larger volume of air to the same extent if it 
were applied to drive an efficient heat-engine, which in its turn 
drove a reversed heat-engine or warming machine to pump up 
heat through a short range from the diffused store of heat which is 
contained in the atmosphere or in the ocean. This is because a 
heat-engine can be arranged to take advantage of the high 
temperature at which heat is produced in the burning of fuel, 
whereas any direct communication of this high-temperature heat 
to a comparatively cool body, such as the air of a room, is thermo- 
dynamically bad. It is interesting, and may some day be useful, 


to recognise that even the most economical of the usual methods 
employed to heat buildings, v^ith all their advantages in respect of 
simplicity and absence of mechanism, are in the thermodynamic 
sense spendthrift modes of treating fuel. 

95. Heat-Engines employing more than one working 
substance: Steam and Ether Engines. So £u- as general 
thermodynamic principles are concerned the choice of working 
substance either in a heat-engine or a refrigerating machine is 
indifferent. The same efficiency is given by one substance as by 
another provided the character and range of the cycle be the same. 
But the consideration that the pressure must be neither excessively 
high nor excessively low often determines whether one or another 
working substance is to be preferred. Vaporisable liquids have the 
advantage over air or any other permanent gas that heat can be 
more readily communicated to and extracted from them ; but any 
such liquid has a comparatively limited range of temperature within 
which it is practicable for it to work. The efficiency of the steam- 
engine is, as we saw in § 68, largely conditioned by the fact that 
the upper limit of temperature cannot well exceed or even reach 
400° Fah. This prevents full advantage being taken of the high- 
temperatui^e heat which is generated in the combustion of fuel in 
boiler furnaces ; and in this respect an air-engine has the superiority 
that in it a much higher temperature can be reached, since in a gas 
the connection of pressure with temperature is arbitrary. On the 
other hand a more volatile liquid than water would be even less 
suitable for use at high temperatures, unless indeed a large amount 
of super-heating were employed. Going to the other end of the 
range, it will be seen by reference to the table of pressure and 
temperature for steam that a steam-engine is not well fitted to take 
full benefit of the low temperature which may be reached when 
there is condensing water at hand. A more volatile liquid would 
do this better, because its vapour could be expanded to the 
bottom of the range of temperature without making the pressure 
fall inconveniently low. With steam complete expansion would 
be useless, because in the last stages of the expansion the pressure 
would barely suffice to move the piston against its own frictional 
resistance ; and therefore the indicated work which would be saved 
by completing the expansion would contribute nothing to the 
output of the engine. 


For this reason it has been proposed to use what is called a 
"binary" heat-engine, that is, an engine with two working fluids, 
one to work through the upper part of the range, and another — a 
more volatile fluid — to work through the lower part. The less 
volatile fluid, namely water, after being evaporated in a boiler and 
after doing work in its cylinder is condensed by passing through 
tubes in a vessel containing the more volatile fluid, to which it 
rejects heat. The more volatile fluid is thereby evaporated and 
does work in another cylinder, after which it is passed into a 
sur£BM^-condenser supplied with cold circulating water. A binary 
engine using ether as the more volatile fluid was introduced by 
Du Tremblay about 1850 \ and the type has more than once been 
revived on a small scale '. 

The same principle of binary action is also applied in refrige- 
rating machines when very intense cold is to be produced for such 
purposes as the liquefaction of the permanent gases. 

96. TranemiBsion of Power by CompreMed Air. A 

brief reference may be made in passing to the process, used on a large 
scale in Paris and elsewhere; of distributing power from central 
stations by compressing air there and conveying the compressed 
air through pipes to the places where it is to be used in driving 
engines, which are generally of the piston and cylinder type. 

Imagine the compression to be performed exceedingly slowly, 
in a conducting cylinder, so that the air within may lose heat 
by conduction to the atmosphere as fast as heat is generated by 

Pio. 8S. 

1 See Min. Proe. Imt. C. jB., Vol. XTin. p. 288. Alao Rankine'a Steam-Engine, 
p. 444. 

■ See Min. Proe, Imt. C. E., Vol. oxn., 1898, pp. 481, 482. 


compression; the process will in that case be isothermal, at the 
temperature of the atmosphere. Imagine further that the com- 
pressed air is distributed without change of temperature, and that 
the process of expansion in the consumer's engine is also indefi- 
nitely slow and consequently isothermal. In that case (if we 
neglect the losses caused by friction in the pipes) there would 
be no waste of power in the whole process of transmission. The 
indicator diagram would be the same, per lb. of air, in the com- 
pressing engine as in the consumer's engine, namely fcae (fig. 38) 
in one and eacfin the other, dc being an isothermal line. 

Imagine, on the other hand, that compression and expansion 
are both adiabatic — a state of things which would be approximated 
to if they were performed very quickly. Then the diagram of the 
compression is /c&d (fig. 39) and that of the consumer's engine is 

Fio. 39. 

Fio. 40. 

eadf (fig. 40), cb and ad being adiabatic lines. The change of 
volume of the compressed air from eb to ea occurs through its 
cooling in the distributing pipes, from the temperature produced 
by adiabatic compression down to the temperature of the atmo- 

Fio. 41. 


sphere. Superposing the diagrams as in fig. 41 and sketching an 
isothermal line between a and c (both of which are points at 
atmospheric temperature) we see that the use of adiabatic com- 
pression involves a waste of power which is measured by the area 
chay while the use of adiabatic expansion by the consumer involves 
a further waste measured by acd. 

In practice the compression ccmnot be made strictly isothermal 
for want of time. The temperature of the air is prevented as far 
as possible fix>m rising during compression by injecting water into 
the compressing cylinder, and in this way the curve which would 
be PF =5 const, if isothermal and PF^'*^ const, if adiabatic takes 
an intermediate position between ca and ch (as examination of the 
actual indicator diagram shows), and may be roughly expressed by 
the equation 

PF^« = const. 

Again, the waste of power in compression may be reduced by 
dividing the process into two or more stages (performed in two or 
more successive cylinders) and cooling the air between one stage and 
the next. In this way a stepped compression curve such as cghijk 

Fio. 42. 

(fig. 42) can be obtained which approximates more nearly to the 
isothermal curve ca, and the loss is consequently reduced by the 
amount of the cross-hatched area. The saving so effected is con- 
siderable when air is highly compressed. 

Similar devices may be used by the consumer to make the 
expansion curve in his engine approximate more nearly to the 
isothermal line : that is, he may inject water or use a compound 
engine, allowing the air time to take up enough heat to restore it 
more or less nearly to atmospheric temperature between one stage 
E, 9 


of expansion and the next. By these means the efficiency of the 
tiansmitting system as a whole (neglecting all losses due to fric- 
tion in the distributing pipes, in the valves of the engines, &c.) 
may be made to approximate to unity. 

There is, however, another point to be considered If the 
temperature be allowed to fall materially during expansion the 
same difficulties present themselves as were referred to above in 
speaking of refrigerating machines : the expanding air tends to 
deposit dew or even snow. To prevent this the practice is often 
followed of passing the compressed air through a stove or 
^'preheater'* in order to raise its temperature just before it is 
allowed to expand, and so prevent the deposit of frozen moisture. 
When " preheaters '' are used the extra heat which they supply is 
of course itself partly converted into work \ 

^. On the Babject of transmission of power by compressed air reference should be 
made to papers by Prof. Kennedy, Brit, Atsoe. Rep. 1889, p. 448, and Prof. 
Nicholson, Engintering^ July 7, 1898. See also Prof. Peabody's ThermodynamU* 
of the Steam-Engine, Chap. xx. 



97. Compariion of actual and ideal indicator dia^^rami. 

We have now to consider in what respects the action of steam in 
a real engine differs from the ideal action described in § 71 of 
Chapter III., where a hypothetical engine was considered in which 
the cycle of operation was as near an approximation to Camot's as 
could be reached without the use of adiabatic compression. An 
engine imagined to work in the manner there described, and 
having an indicator diagram of the type shown in fig. 17, where 
the expansion is adiabatic and complete, forms a useful standard 
with which to compare real engines. Their efficiency is always 
less, for reasons which will be discussed in this chapter. 

In the first place, the expansion in real engines is not (except 
in rare cases) complete : the steam at release has a pressure that 
is higher than the pressure in the condenser, if the engine is a 
condensing engine, or higher than the pressure of the atmosphere 
if the engine is non-condensing. Reasons for this have been 
already indicated: complete expansion would increase the bulk 
and weight of the engine ; the work done by the steam in the 
last stages would add nothing to the net mechanical output for 
it would be used up in overcoming the friction of the piston; 
further, complete expansion would aggravate certain evils to be 
described later which arise from the cooling of the cylinder during 
expansion and exhaust. The effect which incompleteness in the 
expansion produces by itself on the efficiency of the engine has 
already been considered in reference to the indicator diagram, 
fig. 18, and to the entropy-temperature diagram, fig. 29 (§ 88). 



Other features of diflference are most conveniently noticed by 
comparing stage by stage the ideal diagram of fig. 18 with a 
diagram taken firom a real engine. In the action to which figs. 17 
and 18 refer it was assumed — (1) that the steam was supplied 
in the dry saturated state, and had during admission the full 
(unifOTm) pressure of the boiler Pi ; (2) that there was no transfer 

Ab$olut« Vaeuum 

"FiQ, 43. Typical Indicator Diftgram from a Condensing Steam-Engine. 

of heat to or from the steam except in the boiler and in the 
condenser ; (3) that after more or less complete expansion all the 
steam was discharged by the return stroke of the piston, during 
which the back pressure was the (uniform) pressure in the con- 
denser Pa ; (4) that the whole volume of the cylinder was swept 
through by the piston. It remains to be seen how far these 
assumptions are untrue in practice, and how the eflSciency is 
affected in consequence. 

The actual conditions of working differ from these in the 
following main respects, some of which are illustrated by the 
practical indicator diagram of fig. 43, which is taken fi:om an 
actual engine. 

98. Wire-drawing during Admiraion and Exhaust. 

Owing to the resistance of the ports and passages, and to the 
inertia of the steam, the pressure within the cylinder is less than 
Pi during admission and greater than Pj during exhaust. 

Moreover Pi and Pj are themselves not absolutely uniform, and 
Pj is greater than the pressure of steam at the temperature of the 
condenser, on account of the presence of some air in the condenser. 
The presence of air is accounted for partly by its entering the 


boiler dissolved in the feed water, and pai'tly by its leaking into 
the cylinder and other parts of the engine at times when the 
pressure within is less than the pressure of the atmosphere. 

During admission the pressure of steam in the cylinder is less 
than the boiler pressure by an amount which often increases a 
little as the piston advances, on account of the increased velocity 
of the piston's motion and the consequently increased demand for 
steam. When the ports and passages offer much resistance the 
steam is expressively said to be " throttled " or " wire-drawn." Wire- 
drawing of steam is in fact a case of imperfectly resisted expan- 
sion (§ 50). The steam is dried by the process to a small extent, 
as was shown in § 76, and if initially dry it becomes superheated. 
In an indicator diagram wire-drawing causes the line of admission 
to lie below a line drawn at the boiler pressure, and generally to 
slope a little downwards. In fairly good practical instances the 
mean absolute pressure during admission is about nine-tenths oi 
the pressure in the boiler. With a long steam-pipe or a badly 
designed valve the fell of pressure may be greater, and the eflFect 
is aggravated when the steam is allowed to become wet by having 
the pipe insuflSciently "lagged" with some material which is a 
poor conductor of heat. Even under the best conditions some oi 
the steam is condensed on its way to the engine by loss of heat 
from the pipe. This water, as well as any water that may be 
present through "priming" on the part of the boiler, may be 
more or less completely removed by the use of what is called a 
" separator," but usually the steam is to some extent wet when 
it enters the cylinder, notwithstanding the slight tendency that 
wire-drawing has to dry it. 

Again, during the exhaust the actual back-pressure exceeds 
the pressure in the condenser by an amount that depends on 
the freedom with which the steam makes its exit from the 
<5ylinder. In condensing engines with a good vacuum the back- 
pressure is often as much as 3 lbs. per square inch and even 
more, and in non-condensing engines it is 16 to 18 lbs. in place 
of the mere 14*7 lbs. or so which is the pressure of the atmosphere. 
The excess of back-pressure may be greatly increased by the 
presence of water in the cylinder. The effects of wire-drawing 
do not stop here. The valves open and close more or less slowly ; 
the points of cut-ofif and release are therefore not absolutely 
jsharp, and the diagram has rounded corners at b and c in place 


of the sharp angles which mark those events in fig. 18. For this 
reason release is allowed in practice to begin a little before the end 
of the forward stroke, hence the toe of the diagram takes a 
form like that shown in fig. 43. The sharpness of the cut-off, 
and to a less extent the sharpness of the release, depends greatly 
on the kind of valves and valve-gear used ; valves of the Corliss 
type, for instance, which will be described in a later chapter stop 
the admission of steam more suddenly than the ordinary slide 
valve does and therefore produce a more sharply defined diagram. 

99. Clearance. When the piston is at either end of its 

stroke there is a small space left between it and the cylinder cover. 

This space, together with the volume of the passage or passages 

leading thence to the steam and exhaust valves, is called the 

clearance. It constitutes a volume through which the piston does 

not sweep, but which is nevertheless filled with steam when 

admission occurs, and the steam in the clearance forms a part of 

the whole steam which expands after the supply from the boiler 

is cut off. It AC he the volume swept through by the piston up 

to release, OA the volume of the clearance, and AB the volume 

swept through during admission, the apparent ratio of expansion 

. AC . ^^. 1 .• • OA+AC 
IS -T-„ , but the real ratio is ^ . p . 

Clearance must obviously be taken account of in any calcula- 
tion of curves of expansion. It is 
conveniently allowed for in indicator 
diagrams by shifting the line of no 
volume back through a distance corres- 
ponding to the clearance in the manner 
illustrated in fig. 44. In actual engines 
the volume of the clearance OA is 
usually from -fis to -^ o( the volume of 
the cylinder. Its size depends largely 
on the kind of valve that is used. As a rule small engines have 
relatively more clearance than large ones. 

100. CompreMion. Clearance affects the thermodynamic 
eflSciency of the engine chiefly by altering the amount of steam 
that is consumed per stroke, and its influence depends materially 
on the extent to which the compression of part of the steam 
during the return stroke, referred to in § 71, is carried on. If 


Fia. 44. 

Effect of Clearance. 


there were no compression: if» in other words the exhaust pipe 
leading to the condenser or to the atmosphere were left open 
throughout the whole of the back stroke, at the end of that stroke 
the clearance space would have nothing more in it than steam at 
a pressure equal to the back-pressure, and consequently at the 
next admission enough steam would have to be drawn from the 
boiler to bring up the pressure in the clearance as well as to fill 
the volume which is swept through by the piston up to the point 
of cut-oflf. With compression this cause of waste is more or less 
completely avoided. During the back stroke the process of exhaust 
is discontinued before the end as at (2 in fig. 43, and the steam 
remaining in the cylinder is compressed. The cushion of steam 
thus shut in finally occupies the volume of the clearance; and by 
a proper selection of the point at which compression begins the 
pressure of this cushion may be made to rise just up to the 
pressure at which steam is admitted when the valve opens. This 
may be called complete compression, and when it occurs the 
existence of clearance has no direct effect on the consumption of 
steam nor on the eflSciency ; for there is then simply a permanent 
cushion which is alternately expanded and compressed without 
net gain or loss of work, in addition to the working steam 
proper, which on admission fills the volume AB (fig. 44), and 
which enters and leaves the cylinder in each stroke. But if 
compression be incomplete or absent there is, on the opening of 
the admission valve, an inrush of steam to fill up the clearance 
space. This increases the consumption to an extent which is 
only partly counterbalanced by the increased area of the diagram, 
and the result is that the efficiency is reduced. The action is, 
in fact, a case of unresisted expansion (§ 50), and consequently 
tends, so far as its direct effects go, to make the engine less 
than ever reversible. It is to be noted, however, that by any 
imresisted expansion of this kind the entering steam is dried to 
some extent, and this helps in a measure to counteract a cause of 
loss which will be described below. Incidentally, compression has 
the mechanical advantage that it obviates the shock which the 
admission of steam would otherwise produce, and increases the 
smoothness of running by giving the piston work to do while its 
velocity is being rapidly reduced — an action which receives the 
name of "cushioning." 

The opening of the steam valve for admission being a some- 


what gradual process, it generally begins before the back stroke is 
quite complete, in order that the valve may be widely enough open 
to let the steam in freely when the piston begins to move forwards. 
The valve is then said to have lead, and the effect is to produce 
what is called pre-admissioTi^ Pre-admission tends to increase the 
mechanical effect of cushioning which has just been referred to. 

101. Cushion Steam and Cylinder Feed. In dealing 
with the influence of clearance, whether the compression be 
complete or incomplete or even altogether wanting, it is convenient 
to think of the working substance in the cylinder as made up of 
two parts, namely (1) the part that has been shut up in the 
clearance from the previous stroke, and (2) the part that is freshly 
supplied from the boiler. For brevity we shall refer to these in 
what follows as (1) the cushion steam, and (2) the cylinder feed. 
During expansion the whole quantity of working substance in 
the cylinder is the sum of these two; during compression the 
cushion steam only is present. 

102. Influence of the Cylinder Walls. Condensation 
and Re-evaporation in the Cylinder. Generally by far the 
most important element of difference between the action of a 
real engine and that of our hypothetical engine is that which 
was alluded to at the end of Chapter I., the difference, namely, 
which proceeds from the fact that the cylinder and piston are not 
non-conductors. As the steam fluctuates in temperature in the 
phases of admission, expansion and exhaust there is a complex 
give-and-take of heat between it and the metal it touches, and the 
effects of this, though not very conspicuous on the apparent form 
of the indicator diagram, have an enormous influence in reducing 
the efficiency by increasing the consumption of steam. Attention 
was drawn to this action by Mr D. K Clark as early as 1855 S 
and the results of his experiments on locomotives were confirmed 
and extended in 1860 by Mr Isherwood's trials of the engines of 
the United States steamer " Michigan'." Rankine in his classical 
work on the steam-engine notices the subject only very briefly, 
and takes no account of the action of the cylinder walls in his 

^ Railway Machinery ^ or art. STEAV-ENonns, Ency» BriU, 8th edition. See also 
Min. Proe. Irut, C. E,, Vol. Ixxii. p. 275. 

^ See Isherwood's Experimental ReseareJies in Steam Engineering, Philadelphia, 
1863. This important work describes a great number of experiments, under- 
taken at a time when engineers in general were but little alive to their value. 


calculations. Its importance has now been established beyond 
dispute, notably, among early experiments, by those of Messrs 
LoriQg and Emery on the engines of certain revenue steamers of 
the United States^ and by a protra,cted series of investigations 
carried out by M. Bfallauer and other Alsatian engineers under 
the direction of Him", whose name should be specially associated 
with the rational analysis of engine tests, and who was one of the 
first to recognise the losses that result from condensation of steam 
on the surface of the cylinder. The evidence afforded by these 
experiments has been amply confirmed by an immense number of 
trials made on all kinds of engines and under every variety of 
working. In the next chapter some account will be given of how 
steam-engines are experimentally examined and how, from the 
observed behaviour of the steam, we may deduce the exchanges 
of heat which occur between the steam and the cylinder through- 
out the stroke. The following is, in general terms, what experi- 
ments with actual engines show to take place. 

When steam is admitted at the beginning of the stroke, it finds 
the metallic surfaces of the cylinder and piston chilled by having 
been exposed to low-pressure steam during the exhaust of the 
previous stroke. A portion of it is therefore at once condensed, 
and, as the piston advances, more and more of the chilled cylinder 
sur&ce is exposed and more and more of the hot steam is con- 
densed. At the end of the admission, when communication with 
the boiler is cut off, the cylinder consequently contains a film of 
water spread over the exposed surface, in addition to saturated 
steam. The boiler has therefore been drawn upon for a supply 
of steam greater than that which corresponds to the volume of the 
admission space. The importance of this will be obvious from the 
fact that the steam which is thus condensed during admission 
generally amounts to 30 and often even to 50 per cent, of the 
whole quantity that comes over from the boiler. Very rarely is 
it less than 25 per cent, and as much as 69 per cent, has been 
recorded in trials of a small engine*. 

^ An abstract of Messrs Lorind; and Emery's reports is given in Engineering, 
Vols. xix. and zzi., and in Mr Maw's Recent Practice in Marine Engineerirjig, 

^ Butt. 8oc. Industr. de Mulhmue, from 1877. 

> In papers by OoL English {Proc. Inst. MecK Eng. Sept. 1887, Oct. 1889, May 
1892), which describe experiments on this subject, and give the amounts of initial 
condensation which have been found in trials by a number of independent 
observers. In several cases the amount is over 60 per cent. 


Then, as expansion begins, more cold metal is uncovered, and 
some of the remaining steam is condensed upon it. But the 
pressure of the steam now falls, and the layer of water which has 
been previously deposited begins to be re-evaporated as soon as 
the temperature of the expanding steam &lls below that of the 
liquid layer. Hence, on the whole, the amount of water present 
increases during the earliest part of the expansion, but a stage is 
soon reached when the condensation which occurs on the newly 
exposed metal is balanced by re-evaporation of older portions of 
the layer. The percentage of water present is then a maximum ; 
and from this point onwards the mixture of steam and water 
present in the cylinder becomes more and more dried by re-evapo- 
ration of the layer. 

103. Re-eyaporation continued durinfl^ the eachauft 

If the amount of initial condensation has been small this re- 
evaporation may be complete before release occurs. Very usually, 
however, there is still an undried layer at the end of the forward 
stroke, and the process of re-evaporation continues during the 
return stroke, while exhaust is taking place. In extreme cases, if 
the amount of initial condensation has been very great, the 
cylinder walls may fail to become quite dry even during the 
exhaust, and a residue of the layer of condensed water may either 
be carried over as water into the condenser, or, if the exhaust 
valves are not arranged so that it can be discharged, this unevapo- 
rated residue may gather in the clearance space, and in very bad 
cases may even require the drain-cocks to be left open to allow of 
its escape. When any water is retained in this way the initial 
condensation is enormously increased, for the hot steam then 
meets not only comparatively cold metal but comparatively cold 
water when it enters the cylinder. The latter causes much 
condensation, partly because of its high specific heat, and partly 
because it is brought into intimate mixture with the entering 

Apart, however, from this extreme case, whatever water is 
re-evaporated during expansion and exhaust takes heat from the 
metal of the cylinder, and so brings it into a state that makes 
condensation inevitable when steam is next admitted from the 
boiler. It is in fact the condensation of the layer and its re- 
evaporation, wheth^r during expansion or during exhaust, that is 


the means of exchange of heat between the metal of the cylinder 
and the working substance. Mere contact with low-pressure 
steam during the later stages of expansion and during the exhaust 
stroke would cool the metal but little, for communication of heat 
between dry metal and any gaseous substance is slow even when 
the difference of temperature between them is large. The cooling 
which actually occurs is due mainly to the re-evaporation of the 
condensed water. Thus if an engine were set in action, after 
being heated beforehand to the boiler temperature, the cylinder 
would be only slightly cooled during the first exhaust stroke, 
and little condensation would occur during the next admission. 
But the metal would be more cooled in the subsequent expansion 
and exhaust, since it would part with heat in re-evaporating this 
water. In the third admission more still would be condensed, and 
so on, until a permanent regime would be established in which 
condensation and re-evaporation were exactly balanced. The same 
permanent regime is reached when the engine starts cold. 

However early the re-evaporation of the condensed film is 
completed it results in some chilling of the cylinder walls, leaving 
them to be re-heated by condensation of freah steam in the next 
stroke. The evils of initial condensation are greater the later this 
re-evaporation is completed. If the steam in the condensed layer 
is all evaporated before the release but little further cooling of the 
metal will occur during the exhaust stroke : if water remains to 
be evaporated during exhaust the whole action of the sides is 
intensified. It is only in exceptionally fovourable cases that the 
water condensed during admission is completely evaporated before 

104. WetneM of the worUnfl^ iteam. Should the supply 
of steam be itself wet — ^apart fix>m the wetness which it acquires 
during admission on meeting the colder metal of the cylinder, — 
the re-evaporation will take longer to be completed and conse- 
quently the action of the metal will be increased. 

During expansion the working fluid is wet for two reasons, 
first because the cylinder and piston are not non-conductors and 
have consequently condensed a part of the fluid on them during 
its admission, and secondly because even under adiabatic conditions 
the expansion implies some condensation, as was pointed out 
in § 65. The wetness which is due to the action of the walls is 


superficial ; a film of water forms on the metallic surfaces. It may 
be conjectured, on the other hand, that the water which expansion 
itself produces rather takes the form of a mist of minute particles 
scattered throughout the whole volume. There are no experi- 
mental means of distinguishing between the two forms which the 
water may take, and the distinction would in any case have little 
interest What we have to do with at all stages is simply a 
mixture, in varying proportion, of steam and water. Water in 
the form of mist — ^if anything of the kind is formed — ^would be 
much less easy to evaporate than water deposited upon the walls, 
and the fact that in some trials the fluid is apparently quite dry 
at the end of expansion rather indicates that when water is formed 
it collects wholly or mainly on the solid surfaces*. 

106. Graphic Representation^ on the Indicator Dia- 
gram^ of the water present during^ expansion. In testing 
engines, by methods which will be described in the next chapter, 
the amount of steam is measured which passes through the 
cylinder per stroke — that is, the quantity which we have called 
the "cylinder feed." The whole quantity of steam and water present 
during expansion is the cylinder feed plus the cushion steam. To 
estimate the amount of the cushion steam we take on the indicator 
diagram a point after compression has begmi, affcer the exhaust 
valve has become completely closed, and note the pressure and the 
volume there, remembering that the true volume is the sum of 
the uncompleted portion of the stroke and the clearance. From 
this pressure and volume the quantity of the cushion steam is readily 
calculated, assuming that the steam is simply saturated and that 
no water is present when compression begins. As a rule, this 
assumption is probably correct: occasionally the cushion steam 
may be wet, which would make its amount greater, but in most 
cases the supposition that the steam is dry when compression 
begins may be accepted as involving at least no serious error. The 
total quantity of steam in the cylinder during expansion is next 
found by adding the amount of this cushion steam to the 
cylinder feed. A " saturation curve " can then be drawn on the 

^ In this eonneotion reference should be made to the observations of Mr Bryan 
Donkin made by means of an apparatos which he has called a *' revealer.'* See his 
papers " Snr les formes partioolieres prises par Teau dans les cylindres de m a chine s 
A yapear" {Revue UniveneUe des Mines, 1898, p. 276^ Engineering, Jane 30, 
1893), and *< Experiments on the Condensation of Steam'* (Min, Proc. Imt, C. E. 
Vol. cxv., 1883). 


indicator diagram to show the volume which this total quantity 
would fill if it were dry and saturated at each pressure reached 
during the expansion. An example is shown in the indicator 





', <!\ 





I % 




\ 1 

c- -^v 


i ' 

^^ >^,^ 









^^. ^***'**v»^ 


fV, 20 


^Sffff,^ ^^**«*„^ 


i Atmospheric Line "'"^Jgjjii.^ — ■ — *^ 


r ■ • •^^>-— -IT 




0-6 0-8 10 

Volume in cubic feet 
Fio. 45. 

diagram of fig. 45, where SS is the saturation curve. In drawing 
this line the axis of no volume is to be taken to the left of the 
diagram which the indicator traces, by a distance which represents 
the volume of the clearance. Then if a horizontal line ABS be 
drawn to intersect the expansion curve at any point B, AB is the 
actual volume which the expanding mixture filled at this pressure, 
AS is the volume it would have filled if dry and saturated ; BS is 
the volume that is lost by wetness. Hence the proportion of water 


in the mixture is sensibly -j^, and the drjmess q is -j^. Thus 

the proportion of water present at any stage of the expansion is 

determined and is shown in the diagram. 

Fig. 45 relates to a real case — ^a trial, by the author, of a small 

engine of the marine type. The amount of cylinder feed per 

single stroke was 0*0404 lbs. The pressure at the point D was 

found to be 4 pounds per square inch, and the volume there was 

0*12 cub. ft. Since the volume of 1 lb. at that pressure is 90'4 

cub. ft., it follows that the amount of cushion steam was 0*0013 lbs. 

This gives a total of 0*0417 lbs., for which the curve SS is drawn. 

By measuring values of -j-^ at points along the curve it is found 

that the proportion of water in the mixture was 52 per cent, at 
cut-off, then increased to about 55 per cent, during the early 
stages of expansion, then became less and finally sank to 37 
per cent, just before release. 


Again, knowing the wetness of the mixture at the point of 
cut-ofif we may draw an adiabatic line through that point using 
the equation Pt^« constant with a suitable value of n (see § 66). 
This curve will in general be found to lie a trifle above the actual 
expansion curve at first, but to cross it early and lie distinctly 
below it towards the end of expansion. This is because the metal 
continues for some time after cut-ofif to take heat firom the working 
fluid, but later gives up heat to it through the re-evaporation 
of the condensed film. 

By comparing the adiabatic with the actual expansion curve it 
is possible to examine the give-and-take of heat between the metal 
and the working fluid. But this is more conveniently done after 
the entropy-temperature curve has been drawn, as will be presently 

When tests of compound engines are in question it is useful 
to modify the construction shown in fig. 45 by separating the 
cylinder feed firom the cushion steam, and drawing the diagram 
for the former. This allows a combined diagram for the several 
cylinders to be drawn, along with a single saturation curve* The 
reason is that the amount of cylinder feed is the same for both 
or all the cylinders, whereas the amount of cushion steam may 
be very difiTerent. An example of thia construction will be given 
later in dealing with compound engine trials. 

106. Uie of the Entropy-Temperature diagram in 
exhibiting the behayiour of steam during expansion and 
the exchanges of heat between it and the cylinder walls. 

In the entropy-temperature diagram, fig. 46, let ab be drawn at 
the temperature which corresponds to the pressure at the point of 

cut-oflf, and let it be divided at c so that -r represents the pro- 
portion of dry steam to water in the total quantity of working 
fluid present in the cylinder. Similarly, at any lower tempera- 
tures reached during expansion let lines a'b\ a"V' be divided at 
points c', c" in the proportion of steam to water then present, 

at the corresponding pressure in the indicator diagram (fig. 45). 
In this way the curve cc'c" is determined, which represents the 



real process of expansion, and this is readily compared with the 
ideal adiabatic process represented by the straight vertical 

Fig. 46. 

line eg. Taking &' as the point of release the diagram may be 
continued by drawing a • constant- volume curve as described in 
§ 88. In the first stages of expansion, namely from c to & in the 
sketch, the proportion of water in the cylinder is increasing, and 
the heat abstracted by the cylinder walls from the steam is the 
area cghc'. From this point onwards the steam becomes drier, 
and ts^es up heat from the metal, the whole amount recovered up 
to the point of release being the area c'c'^eh. It will be seen that 
a diagram of this type is particularly well fitted to allow the 
transfer of heat between metal and fluid to be traced throughout 
all stages of the expansion, the heat given up or recovered in any 
part of the process being equal to the area under the correspond^ 
ing portion of the expansion curve ccV. When this curve slopes 
down to the left heat is passing from the steam to the metal ; when 
it slopes at the right the exchange is the other way. The heat 
abstracted from the steam during compression and admission is 
nearly equal to the area fbcff — nearly, but not exactly, because all 
the condensation in these stages does not occur at the pressure 
of cut-ofif. During compression condensation is going on at lower 
pressures because the temperature of the cushion steam — ^necessarily 
rising with the pressure — is being raised above the temperature 
to which the walls have been chilled during exhaust. 


107. Thermodsrnamic IiOm due to Initial Condensation. 

From a thermodynamic point of view all initial condensation of the 
steam is bad, for, however early the film of water be re-evaporated, 
this can take place only after its temperature has cooled below that 
of the boiler. The process consequently involves a misapplication 
of heat, since the substance, after parting with high-temperature 
heat, takes it up again at a temperature lower than the top 
of its range. This causes a loss of efficiency and the loss is 
greater the later in the stroke re-evaporation occurs. The heat 
that is drawn from the cylinder by re-evaporation of the condensed 
film becomes less and less effective for doing work as the end of 
the expansion is approached, and finally, whatever evaporation 
continues during the back stroke is an unmitigated source of 
waste. The heat it takes from the cylinder does no work^; its 
only effect, indeed, is to increase the back-pressure by augmenting 
the volume of steam to be expelled. A small amount of initial 
condensation reduces the efficiency of the engine but little ; a 
large amount causes a much more than proportionally larger loss. 

108. Action of a Steam-jacket The action of the cy- 
linder walls is increased by any loss of heat which the engine may 
suffer by radiation and conduction from its external surface. The 
entering steam has then to give up enough heat to provide for 
this waste, as well as enough to produce the subsequent re-evapo- 
ration of the condensed film. The consequence is that more steam 
is initially condensed. The loss of efficiency due to the action of 
the cylinder walls will therefore be greater in an unprotected 
cylinder than in one which is well lagged or covered with non- 
conducting material. On the other hand, if the engine have a 
steam-jacket the deleterious action of the walls is reduced. The 
working substance is then on the whole gaining instead of losing 
heat by conduction during its passage through the cylinder. The 
jacket accelerates the process of re-evaporation, tending to make 
it occur while the temperature and pressure of the steam 
are still comparatively high. After the process of re-evapo- 
ration is complete the jacket cannot superheat the steam in the 
cylinder to any material extent, for conduction and radiation 

^ Unless, of course, the cylinder in question is one of a compound series, and 
the steam that leaves it passes on to another cylinder to undergo fturther expansion 


between dry steam and the metal of the cylinder are incompetent 
to cause any considerable exchange of heat. The earlier, there- 
fore, that re-evaporation is complete the less is the metal chilled, 
and the less is the subsequent condensation. But after re- 
evaporation is completed the steam in the jacket continues to 
give heat to the metal during the remainder of the cycle, and 
so warms it to a temperature more nearly equal to that of the 
boiler steam before the next admission takes place. 

Thus a steam-jacket, though in itself a thermodynamically 
imperfect contrivance, inasmuch as it supplies heat to the working 
substance at temperatures lower than the top of the range, acts 
beneficially by counteracting, to some extent, the more serious 
misapplication of heat which occurs through the alternate cooling 
and heating of the cylinder walls. The heat which a jacket com- 
municates to the working steam often increases the power of the 
engine to an extent far greater than corresponds to the extra 
supply of heat which the jacket itself requires. A jacket has the 
obvious drawback that it increases waste by external radiation, 
since it both enlarges the area of radiating surface and raises its 
temperature; notwithstanding this, however, many experiments 
have shown that the influence of a steam-jacket on the efficiency 
is good, especially in slow running engines and in engines where 
there is a large ratio of expansion in a single cylinder. This is to 
be ascribed to the fact that it reduces, though it does not entirely 
remove, the evils of initial condensation. To quote once more 
Watt's words, the jacket does good by helping to keep the cylinder 
as hot as the steam that enters it. To be effective, however, jackets 
must be well drained and kept full of " live " steam, instead of 
being, as many are, traps for condensed water or for air. The action 
is kept up by condenscition of steam in the jacket itself. When the 
jacket is acting effectively the amount of steam which is condensed 
in it generally ranges from about 7 to 12 per cent, of the whole steam 
supply. The most economical treatment of the jacket-water is 
to allow it to drain directly back into the boiler. In some cases 
the activity of the jacket has been secured by letting all the steam 
supply pass through the jacket on its way to the cylinder, an 
arrangement which makes particular care necessary to prevent the 
water which is formed in the jacket from passing into the cylinder. 

We shall refer presently to experiments which show the 
influence of steam-jackets on the efficiency of engines of various 
E. 10 


types. Meanwhile it may be said that in no trials has it appeared 
that a jacket has done harm : in other words the saving of steam 
in the cylinder-feed brought about by the use of a jacket is always 
greater than the amount of steam which the jacket itself uses, and 
in many instances the net saving is as much as 10 or 20 per cent. 
The best results are found in cases where, if the jacket were 
absent, the conditions are such as would give rise to much initial 
condensation. In engines which make a great number of strokes 
per minute the influence of the jacket is necessarily small. 

The advantage of the jacket may be increased by making its 
temperature higher than that of the steam during admission to 
the cylinder. Re-evaporation of the condensed layer is further 
hastened and afber it is over the jacket gives up but little heat. 
Mr Bryan Donkin has obtained good results in experiments where 
the cylinder of a small engine was kept hot by gas flames, and it 
has been proposed to jacket engines with the hot gases from the 
furnace after these have passed through the boiler-flues \ 

109. Influence of Speedy Size, and Ratio of Expansion. 

It is interesting to notice, if only in general terms, the effects 
which the particular conditions of working in different engines 
may be expected to produce on the loss that occurs through 
the action of the cylinder walls. Initial condensation will 
be increased by anything that augments the range of tempe- 
rature through which the inner surface of the cylinder fluctuates 
in each stroke, or that exposes a larger surface of metal to the 
action of a given quantity of steam, or that prolongs the contacts 
in which heat is exchanged. The influence of time is specially 
important ; for the whole action depends on the rate at which 
heat is taken up and given up by the substance of the metal. 
The changes of temperature which the metal undergoes are in 
every case mainly superficial ; the alternate heating and cooling 
of the inner surface initiates waves of high and low temperature 
in the iron whose effects are sensible only to a small depth ; and 
the faster the alternate states succeed each other the more super- 
ficial are the effects^ In an engine making an indefinitely large 

1 For Mr Donkin'B experixnente'see Min» Proe, InaU C. E., 1889, Vol. xoviii. pt. 4. 

* The temperature of the cylinder walls has formed the subject of an interestmg 
-experimental study by Mr Bryan Donkin, who has examined the general gradient 
of temperature across the walls, both with and without steam in the jacket. See 
liis two papers, Min. Proc, Inst, C. £., 1890 and 1891. 


number of strokes per minute the cylinder sides would behave 
like non-conductors and the action of the working substance would 
1)e adiabatic. 

We may conclude, then, that in general an engine running at 
a high speed will have a higher thermodynamic efficiency than 
the same engine running at a low speed, all the other conditions 
of working being the same in both cases. 

Again, as regards range of temperature, the influence of the 
•cylinder walls will be greater (other things being equal) with high 
than with low pressure steam, and in condensing than in non- 
condensing engines. 

In large engines the action of the walls will be less than in 
small engines, since the proportion of wall sur£9u^ to cylinder 
volume is less. This conclusion agrees with the well-known fact 
that small engines do not readily achieve the economy that is 
reached in many larger forms. 

Cylinder condensation is increased when the ratio of expansion 
is increased, all the other circumstances of working being left 
unaltered The metal is then brought into more prolonged 
contact with low-temperature steam. The volume of admission 
is reduced to a greater extent than the surface that is exposed to 
the entering steam, since that sur£su^ includes two constant 
quantities, the surface of the cylinder-cover and of the piston. 
For these and perhaps other reasons, we may expect that with an 
early cut-off the initial condensation will be relatively large ; and 
this conclusion is amply borne out by experiment. An important 
result is that increase of expansion* does not, beyond a certain 
limit, involve increase of thermodynamic efficiency; when that 
limit is passed- the augmentation of waste through the action of 
the cylinder walls more than balances the increased economy to 
which, on general principles, expansion should give rise, and the 
result is a net loss. It is for this reason more than for any other 
that it is not wise in practice to carry expansion too feir — ^not, in 
general, nearly so far as to be complete. With a given engine, 
boiler-pressure, and speed, a certain ratio of expansion will give 
maximum efficiency. But the conditions on which this maximum 
depends are too complex to admit of theoretical solution ; the best 
ratio can be determined only by experiment. It may even happen 
that an engine which is required to work at a specified power will 
give better results, in point of efficiency, with moderate steam- 




pressure and moderate expansion, than with high steam-pressure 
and a very early cut-off. 

110. Results of Ejcpeiiments with Tarious ratios of 
Expansion. The effect of increased expansion in augmenting 
the action of the sides and so reducing the e£Sciency, when carried 
beyond a certain moderate grade, was clearly shown by the 
American and Alsatian experiments alluded to above. The 
following figures (Table III.), relating to a single-cylinder Corliss 
engine, are reduced from one of Hallauer*s papers * : — 

Table 111. 

Ratio of 

Percentage ol Water present. 

Consmnption of 

Steam per Hoar 

per Indicated 

Honw Power. 


At End of 

At End of 







Here in consequence of the amount of initial condensation in- 
creasing with increased expansion, a maximum of efficiency lies 
between the extreme grades of expansion to which the test 
extends, but the efficiency varies exceedingly little even through 
this wide range. In the American experiments the best results 
were obtained with even more moderate ratios of expansion. The 

Table IV. 

Oonsnmption of 

Batio of Total 

Steam per Hour 


per I. H. P. 












1 Bull Soe, Industr, de Mulhause, May 26, 1880. 



compound engines of the United States revenue steamer " Bache," 
when tested with steam in the jacket of the large cylinder, with 
the boiler-pressure nearly uniform at 80 lb. by gauge, or 96 lb. per 
square inch absolute, and the speed not greatly varied, gave 
results which are shown in Table IV. Here the efficiency is very 
little affected by a large variation in the position of the cut-off, 
but when the ratio of expansion becomes excessive a distinct loss 
is incurred. 

Again — to take a more recent instance, and one relating to a 
very different tj^e of machine — trials made by the late Mr 
Willans with one of his high speed compound non-condensing 
single-acting engines, using steam with an absolute initial pressure 
of 130 lbs., gave these results (Table V.) \ 

Table V. WUlana* Engine (^onrcandensing) : Effect of varying 
if^e expansion^ the initicU pressure and speed being constant 

Batio of Total 

Percentage of Water 
present at end of 

aidmiuion in high- 
presBure cylinder. 

Consamption of Steam 

per Hour per I. H. P. 

















The initial condensation is comparatively small here, mainly in 
consequence of the exceptional speed (404 revolutions per minute), 
and for the same reason the economy in steam consumption is 
remarkably high for a small non-condensing engine. In another 
series of trials in which a compound engine of this type was worked 
with a condenser ^ and with steam at about 170 lbs. (absolute) 
Mr Willans found a slight increase in the steam consumption 
from 14*26 to 14*72 lbs. per hour per I. H. p. when the ratio of 
expansion was increased from 15^ to 20 ; at the same time the 
percentage of water present at cut-off on the high-pressure 

1 Willans on Non-Condensing Steam-Engine Trials. Min. Proe, Intt. C, £., 
March ISSS. 

> Willans on Steam-Engine Trials. Min. Proc, IruU C. £., April 1693. 



cylinder increased from 31 to 37. All these results agree in 
shoeing that the ratio of expansion may be varied through a 
large range with but little influence on the efficiency, because the 
gain that comes of making the expansion more complete is 
counterbalanced by the bad eflfects of increased initial condensa- 
tion. The ratio of expansion which gives a maximum of efficiency 
is never sharply defined, and its value depends much on the initial 
steam-pressure and the particular features of the engine under 

111. Advantage of high speed. The advantage of high 
speed in making the action of an engine more nearly adiabatic 
has been demonstrated by experiment Among the trials de- 
scribed by Mr Willans in his earlier paper are the following two 
sets made with one of his compound non-condensing engines, in 
the first set with an absolute admission pressure of 90 lbs. per 
square inch and 3*2 as the ratio of expansion ; in the second set 
\^ith 130 lbs. pressure and 4*8 as the ratio. In the three trials of 
each set the only thing varied was the speed. 

Table VI. WUlcma^ Nonrcondensing Engine Trials : In/hience 

of Speed, 

Speed; revolutions 
per minnte. 

Percentage of Water 
present at cut-off in 
the high-pressure 

Consumption of 
Steam per Hour 
per I. H. P. abs.) 

I. Trials witii Steam of 
90 lbs. pressure. 

U. TriaU witii Steam of 
180 lbs. pressure. 













The increase of steam consumption as the speed is reduced is 
considerable, and still more marked is the greater initial conden- 
sation. The same features are apparent in the trials quoted below 
(Table VII.) from an extensive series in Mr Willans' second paper ; 
they relate to a condensing engine with an absolute admission 
pressure of 90 lbs. and a very moderate ratio of expansion (4*8). 

Table VII. WilUms' Candefising Engine Trials : Influence of Speed. 

Spaed: rerolations per 





Peroentage of Water present 
St cnt-off in the high-pree- 
Buie ^Under. 





Congnmption of Steam per 
Hoar per I. H. P. (lbs.) 





112. Erpeiiments on the value of the Steam-jacket. 

Abundant evidence of the advantage of the steam-jacket is given 
in Reports of a committee appointed by the Institution of Me- 
chanical Engineers to enquire into the subjects Individual 
figures vary widely, but it appears that the saving usually secured 
by jackets in condensing engines is something like 12 or 15 per 
cent. In non-condensing engines it is less. The following results 
of special trials with condensing engines are stated in the Report. 

Table VIII. Influence of JStean^jacket, 


Total Steam per 

Hour per I. H. P. 




tion of 
feed to 
total con- 



Two-cylinder componnd^. 

Two-cylinder compound^. 

Triple compound K 

Triple compound'. 

rTwo-cylinder compound'. 

(Same engine run non-compound, 
the large cylinder only being used. 

Small single-cylinder^ engine. 










6 ! 



7 ' 


7 i 

1 Proceedings Inst, Mech, Eng. 1889 and 1892. The second report contains a 
useful summary of the results of trials. 

« Prof. 0. Reynold's tests. For particulars see Min. Proc, Inst. C. E., Vol. xcix. 

» Prof. Unwinds tests : Proc, Inst, Mech. Eng. 1892, p. 460. 

4 Mr B. Donkin's tests: Proc. Inst. Mech. Eng. 1892, p. 464. 


In several of these cases, notably in the last, it is remarkable how 
large a net saving of steam is secured by a comparatively small 
consumption in the jackets. In other trials of the same small 
engine, using an earlier cut-off, Mr Donkin found that 8 or 9 per 
cent, used in the jackets was capable of saving as much as 40 per 
cent, of the whole steam. In this instance there was excessive 
initial condensation when the jackets were out of use. 

In compound engines the jackets are most effective when both 
or all of them are filled with steam at the boiler pressure. In 
Prof. Reynold's triple engine trials, it was found that steam of 
the full boiler-pressure (200 lbs. per sq. inch) in all the jackets 
reduced the initial condensation in the second cylinder to about ^ 
or ^ of the amount that occurred without jackets, made the steam 
practically dry before the end of expansion in the second cylinder, 
and almost entirely prevented condensation in the third cylinder. 
Without steam in the jackets the second and third cylinder had 
been very wet, the proportion of water in them being about 
40 per cent, of the whole. Indicator diagrams relating to these 
trials will be found in Chapter VII. 

In Mr Donkin's experiments the temperature of the cylinder 
itself was observed at various points between the inner and outer 
surface, by means of thermometers inserted in small holes drilled 
in the metal. When the jackets were in use the mean temperature 
of the metal was almost equal to that of the steam on admission ; 
when the jackets were not in use it was some fifty degrees lower. 
The temperature as shown by the thermometers was nearly 
uniform irom inside to outside ; for the periodic chilling of the 
innermost layer of metal by re-evaporation of condensed water 
was too superficial to be at all fully exhibited in this way. 

113. Superheating. Superheating the steam before its 
admission reduces the amount of initial condensation, by lessening 
the quantity of steam needed to give up a specified amount of 
heat, and this in its turn lessens the subsequent cooling by re- 
evaporation. That it has a marked advantage in this respect was 
first experimentally demonstrated by Hirn, who found that the 
consumption of steam was reduced fi-om 194 to 16*2 lbs. per 
horse-power-hour in a condensing engine by superheating the 
steam some 80° FaL On general thermodynamic grounds super- 
heating has a slight advantage (§ 85) because it allows a small 



part of the whole heat supply to be taken in at a higher tempera- 
ture than that of the boiler. But the indirect advantage is much 
more considerable. About the year 1860 superheating was fre- 
quently used in marine practice, but it was abandoned, mainly 
on account of difficulties in regard to lubrication. The importance 
of taking mecais to avoid or rather to reduce initial condensation 
was less generally understood in those days than it is now, and 
there is some evidence that the objections to superheating would 
no longer be so serious if the practice were revived. 

So far as land engines are conceiiied, a revival in the use of 
superheated steam may be said to have already begun. Experi* 
ments made in 1892 by the Alsatian Association of Steam Users 
on a large number of engines furnished with superheaters showed 
that superheating effected a saving of coal to the extent of about 
20 per cent, in cases where the superheater was simply placed in the 
boiler flue, so that it enabled what would otherwise be waste heat to 
be utilized, and about 12 per cent., on the average, in cases where 
the superheater was separately fired. Several of the engines tested 
were large, indicating 500 or 600 horse-power, and the superheating, 
which usually amounted to 60° or 80° Fah., appears to have been 
carried on without inconvenience. One of the trials, dealing with 
a triple-expansion Sulzer engine of 300 horse-power records a con- 
sumption of 14*6 lbs. of steam per i. H. p.-hour without superheat- 
ing, and 11*6 lbs. when the steam was superheated 100° Fah. 

The following experiments made by Willans with and without 
superheating in a high speed single-cylinder condensing engine 
cutting off steam at half stroke show that some advantage results 
even under conditions which are not such that much advantage 
could be expected. 

Table IX. WiUana^ Engine with and tvithout Superlteating, 

Initial pressare, lbs. per 
sq. in. absolute. 




Temp, of Steam at ad- 
mission (Fah.). 







Amount of Superheating. 







Percentage of water at out- 







Consumption of Steam per 
Hour per I. H. P. 









^ 114 Advantage of Compound Expansion. The most 
important means in general use of preventing cylinder condensa- 
tion from becoming excessive is the use of compound expansion. 
If the vessels were perfect non-conductors of heat it would be, 
from the thermodynamic point of view, a matter of indifference 
whether expansion was completed in a single vessel or divided 
between two or more, provided the passage of steam from one to 
the other was performed without introducing unresisted expansion. 
In practice, indeed, the transfer of steam from one cylinder to 
another during its expansion cannot be accomplished without 
more or less of wasteful drop in pressure. But the loss that 
this entails is more than counterbalanced by the gain that results 
from the reduced influence of the cylinder walls. Compound 
working acts beneficially by diminishing the range through which 
the temperature of any part of the cylinder-metal varies. For 
this reason the amount of steam initially condensed in the high- 
pressure cylinder of a compound engine is less than if admission 
were to take place at once into the low-pressure cylinder and the 
whole expansion were to be performed there. Further, the steam 
which is re-evaporated from the first cylinder during its exhaust 
does work in the second, and it is only the re-evaporation that 
occurs during the exhaust from the last cylinder that is absolutely 
wasteftil. The exact advantage of this division of the whole range 
of temperature into two parts, or more than two, as compared with 
expansion between the same limits in a single cylinder, would 
scarcely admit of calculation ; but it is easy to see in a general way 
that an advantage is to be anticipated, and experience bears out 
this conclusion. When a compound engine is tested first with 
compound expansion and then with the same grade of expansion 
in the large cylinder alone it is found that more steam is required 
per horse-power-hour in the second case. 

Thus in the American Naval experiments the compound 
engine of the "Bache" when worked as a simple engine used 
24 lbs. of steam per i. H. p.-hour, as compared with about 

20 lbs. when the engine worked compound, with the same boiler 
pressure, the same total expansion, and steam in the jacket in 
both cases. Again, Professor Unwin's tests referred to in Table 
y III. frimish another instance of the same thing: an engine taking 

21 lbs. of steam per I. H. p.-hour when working compound required 
32 lbs. when the large cylinder only was used, no jackets being 
then in action. With steam in the jackets the difference was rather 


less, for the jacket checked that excessive cylinder condensation 
which reduced the efficiency in the non-compound trials. 

The general subject of compound expansion will be considered 
more particularly in a later chapter : at present we are concerned 
with the influence of compounding on efficiency. Experience 
shows that it is only by resorting to compound expansion that the 
economical advantages of high-pressure steam are to be secured. 
When high-pressure steam is used in a non-compound engine the 
waste due to initial condensation is excessive because of the great 
range of temperature through which the metallic surfaces fluctuate 
in every stroke. The necessity for compounding becomes greater 
with every increase of boiler pressure. So long as the initial 
pressure is less than about 100 lbs. per square inch (absolute) it 
suffices to reduce the range of temperature into two parts by 
employing two-cylinder compound engines ; with the considerably 
higher pressures now common in marine practice triple expansion 
is usual and even quadruple expansion is occasionally employed. 

The advantage of three cylinders is unquestionable ; but it is 
doubtful whether — with the existing upper limit of pressure — four 
cylinders give any further saving sufficient to make up for the 
increased cost and complication of the machine. 

116. Summary of Sources of Loss. The principal reasons 
have now been named which make the actual results of engine 
performance diflfer from the results which would be obtained if the 
steam conformed in every respect to the ideal cycle of § 71^ The 
sources of loss may be summarised as follows : — 

(1) Wire-drawing in admission and exhaust. 

(2) Incomplete expansion before release. 

(3) Incomplete compression of the cushion steam, through 
which the clearance becomes a cause of waste. 

(4) The action of the metallic surfaces of the cylinder and 
piston, causing condensation during compression and admission, 
with re-evaporation during expansion and exhaust. 

(5) Radiation and aerial convection of heat from steam pipe, 
valve chest and all hot parts of the engine, including evaporation 
and other escape of heat from condensed water in the hot well. 

(6) Escape of the working fluid by leakage, and leakage of 
air into the condenser. 

(7) Leakage of steam past the piston. 


(8) In compound engines, additional wire-drawing or un- 
resisted expansion in the transfer of steam from one cylinder to 

If in drawing a comparison between the real engine and the 
ideal we take as the lower limit of temperature that of the cold 
water supplied to the condenser instead of the temperature of the 
hot well, we have a further item, namely the loss that comes from 
the pressure in the condenser being higher than the pressure 
corresponding to this lower limit. 

116. Methods of stating the performance of Steam- 
Engines. It remains to state a few of the best results that 
have been obtained in trials of actual engines, from which the 
aggregate eflfect of these several sources of loss may be inferred. 
The methods used in making such tests will be described in the 
next chapter. 

Statements of steam-engine performance may be put in a 
considerable variety of ways. Comparing the work done with the 
total heat which the working fluid takes in we may either 
calculate the thermodynamic efficiency (the work done divided by 
full mechanical equivalent of the heat taken in), or express the 
same idea in slightly different forms, such as by stating the 
number of thermal units used per indicated horse-power-hour. 
One horse-power being 33,000 foot-lbs. per minute, one horse- 
power-hour is 1,980,000 foot-lbs., the heat-equivalent of which is 
2645 thermal units (taking / to be 778 foot-lbs.). 

Thus the relation between these two modes of statement is 
given by the equation 

Efficienc = ^^ 

^ Number of thermal units used per horse-power-hour ' 

In reckoning the work done and the heat supplied it is very 
convenient to express these quantities per lb. of cylinder feed. A 
strict reckoning of the work done in the steam-engine cycle should 
allow for the work spent upon the working fluid in the feed-pump 
(and, in condensing engines, in the air-pump) an item which 
however is so small that account is rarely taken of it. Take for 
instance the case of an engine using say 16 lbs. of steam per 
horse-power-hour, the boiler pressure being 100. lbs. absolute. 
The feed-pump must return to the boiler 16 lbs. of water per 
i.H.P.-hour and the volume of this water is 0*26 cubic feet. 


The work spent upon it in transferring it from the condenser to 
the boiler is therefore 0*26 x 100 x 144 or 3744 foot-lbs., a quantity 
almost negligibly small by the side of the 1,980,000 foot-lbs. 
which represents the work done by the steam. 

The most usual plan followed by engineers in stating the 
results of trials is to give the number of lbs. of steam used per 
i.H. P.-hour. The supply of heat is nearly proportional to the 
supply of steam, and hence a knowledge of the latter gives 
at once a good general idea of the quality of the performance. 
There is very little change in the total heat of steam within the 
range of pressure at which boilers work in practice. 

The most uncertain element in this form of statement is the 
dryness of the steam supply : if the boiler primes badly or if the 
steam is allowed to become very wet on its way to the engine, the 
quantity of heat which is supplied in each lb. of the cylinder feed 
may be seriously reduced, in an ill designed or overworked boiler 
the amount of priming may be serious : under fairly good con- 
ditions it ought to be less, and is probably in general much 
less, than 6 per cent, of the whole supply. Unfortunately the 
amount of priming is difficult in any case to determine accurately 
by experiment 

When the boiler pressure, the feed temperature, and the 
dryness of the supply are known, it is practicable to treat the 
thermodynamic cycle as a whole and to calculate precisely how 
much heat is taken up by each lb. of steam. But even without 
making this calculation a mere statement of the number of lbs. of 
steam used per horse-power-hour is enough to allow a good 
judgment to be formed on the comparative results of different 
engine performances, and it has the advantage of putting results in 
a way that is easy to appreciate and remember. 

117. Efficiency of boiler and fVimace. '' Duty.'' None 
of these modes of statement include the efficiency of the boiler 
and furnace. The performance of a boiler is most usually ex- 
pressed by giving the nupaber of pounds of water at a stated 
temperature that are converted into steam at a stated pressure by 
the combustion of 1 lb. of coal. The temperature commonly chosen 
is 212® F., and the water is supposed to be evaporated under atmo- 
spheric pressure ; the result may then be stated as so many pounds 
of water evaporated from and at 212** F. per lb. of coal. But the 


term "efficiency" may also be applied to a boiler and furnace 
(considered as one apparatus) to express the ratio of the heat 
that is utilized to the potential energy that is contained in 
the fuel. This ratio is, in good boilers, about 0*7. Thus, for 
example, 1 lb. of Welsh coal contains about 15,500 thermal units 
of potential energy, an amount which is equal to the heat of 
production (i) of about 16 lbs. of steam from and at 212°. In 
practice, however, 1 lb. of coal serves to evaporate only about 11 
lbs. of Water under these conditions, or about 9'5 lbs. when the 
feed-water enters, say, at 100° F. and the absolute pressure is 
100 lbs. per square inch. 

The efficiency of the engine multiplied by that of the furnace 
and boiler gives a number which expresses the ratio of the 
heat converted into work to the potential energy of the fuel, — a 
number which is, in other words, the efficiency of the system of 
engine, boiler, and furnace considered as a whole. Instead, 
however, of expressing this idea by the use of the term efficiency, 
engineers are rather in the habit of stating the performance 
of the complete system by giving the number of pounds of coal 
consumed per horse-power-hour. It must be borne in mind that 
this quantity depends on the performance of the boiler as much as 
on that of the engine, and that the difference in thermal value 
between one kind of coal and another makes it, at the best, a rough 
way of specifying efficiency. It is, however, an easy quantity to 
measure ; and to most users of engines the amount of the coal-bill 
is a matter of greater interest than any results of thermodynamic 
analysis. Still another expression for engine, boiler and furnace 
performance taken jointly, similar to this last, is the now obsolete 
term " duty," which is the number of foot-pounds of work done 
for every 1 cwt. of coal consumed. Its relation to the pounds of 
coal per horse-power-hour is this — 

jy^^ ^ 112 X 38000 X 60 

^ Number of lbs. of coal per i. H. p.-hour ' 

A good two-cylinder compound condensing engine of large size, 
supplied by good boilers, consumes about 2 lbs. of coal per horse- 
power-hour; its "duty" is then about 110 millions. 

In the best examples of modem triple-expansion engines 
the consumption of coal is about l^^jj^. per horse- power-hour, 
making the "duty" about 166 millions. 


118. Results of Trials : Non-Condensing Engines. The 

following are some representative results obtained in carefully 
performed trials of good engines. 

In regard to non-condensing engines there are comparatively 
few records beyond the extensive series of tests by Willans on the 
special type of high-speed single-acting engine invented by him. 
Tests by Mr Emery of the single cylinder engines of the U. S. 
Steamer " Gallatin" included some non-condensing trials in which 
the consumption of steam was 25*9 Iba per i.H.p.-hour with 
jackets in use and 30 lbs. without jackets\ The ratio of ex- 
pansion was a little over 4, and the boiler pressure 70 Iba by 
gauge. With the condenser in use, and the jacket, the consump- 
tion fell to 20*5 lbs. In tests by Mr J. W. Hill' three engines 
each with a single cylinder, with valves of the Corliss type, working 
at about 140 horse-power, without jackets, with a boiler pressure of 
96 lbs., making 76 revolutions per minute, and cutting oflf steam 
at about J of the stroke, required 25*9, 249 and 23*9 lbs. of steam 
per l.H.P.-hour respectively when worked non-condensing and 20*6, 
19*5 and 19*4 lbs. when worked condensing. 

It appears then that under such conditions 24 lbs. of steam 
per i.H.p.-hour is a good performance for a non-condensing engine. 
It is interesting to compare this with the supply that would be 
required if the ideal conditions of § 71, including complete adia- 
batic expansion, were realized. In that case the amount of work 
obtainable from 1 lb. of steam is given (§ 78) by the equation 

F=(T,-T,)(l + f-')-T,l0g.^». 

With a boiler pressure of 96 lbs. by gauge the temperature is 
386T. and Ti is 796. Since steam escaping to the atmosphere 
has the temperature 212° F. r^ is 673. By the table in the 


appendix — , which is ^, — ^wi is 1*106. We therefore have 

Tr= (796 - 673) (1 + 1-106) - 673 log. 1-183 

= 259 - 113 = 146 thermal units. 

To produce one horse-power-hour, which is equivalent to 2545 
thermal units, we should therefore, tinder these ideal conditions, 

^ See Peabody's Thermodynamiet of the Steam-Engine, p. 272. 
s Ibid. p. 268. 



require ■ or 17*4 lbs. of steam, instead of the 24 lbs. or so 

which are actually required in these (exceedingly good) perform- 
ances. In other words the actual engine, at^tfllbest, succeeds in 
doing 73 per cent, of the work which it would oBvable to do if 
none of the sources of loss existed which were enuiperated in 

Again, we may consider the thermodynamic cycle as a^nbole 
and compare it with the perfect cycle of Carnot. To do tc 
something must be known or assumed as to the temperature oi 
the feed-water, and we may take the most favourable possible 
case, namely that in which the escaping steam is collected at 
212"" F. as water and is returned to the boiler. In that event the 
heat taken in per lb. of steam would be 

Hi-Jh^ 1184 - 180 = 1004 thermal units. 

The work done per lb. of steam, when 24 lbs. are used per 
horse-power-hour is 



■ = 106 thermal units. 

The efficiency is therefore , ^ . = 01056. 

Compare this with the efficiency of an engine following 
Camot*s cycle, namely 

Ti-Ta 796^673 


= 0155. 

Hence the actual engine's efficiency is 68 per cent, of that of a 
thermod}mamically perfect engine working between the same limits 
of temperature, if we suppose the exhaust steam to be condensed 
at atmospheric pressure and returned to the boiler without loss 
•of heat on the way. The standard of comparison here is of course 
diflferent from the one just used; the calculation of W from 
equation (7) of § 78 may be said to aflford a fairer means of 
contrasting what a steam-engine might do with what it does. 
The important experiments carried out by Willans on high 
speed engines of a special type, to which reference has been 
already made, included non-condensing trials both of single- 
cylinder and of compound engines^ With a small non-com- 

^ Min, Proc. Inst, C. E., Vols, xciii. part 8 and xovi. part 2. 


pound single-cylinder engine making 400 revolutions per minute 
the best result that is recorded was 26 lbs. of steam per indicated 
horse-power-hour, which was obtained when the mean absolute 
pressure during admission was 106 lbs. per square inch and the 
ratio of expansion was about 4^. Higher efficiencies were reached 
in compound trials made at the same speed* With a boiler 
pressure of 100 lbs. per square inch above the atmosphere the 
compound engine took 23 lbs. of steam per horse-power-hour. 
At 135 lbs. per square inch in the boiler the consumption fell 
to 20*36 lbs. in one trial and 20*75 in another. At 165 lbs. per 
square inch in the boiler it fell as low as 19*14 lbs. in two trials 
and was under 19*2 lbs. in two others. Even these very remarkable 
results were surpassed in a few triple-expansion trials, when on 
raising the boiler pressure to 172 lbs. per square inch the con- 
sumption of steam per horse-power-hour was reduced to 18*6 lbs., 
in the mean of three independent and closely accordant measure- 
ments. All these figures refer to non-condensing engines. 

Taking this last record the quantity W calculated as above 
fix)m the equation in § 78, is 183 thermal units. The actual 
engine got an amount of work out of each lb. of steam equivalent 

to YoT ^^ 13^ thermal units, which is 75 per cent, of TF. In most 

of the trials at lower pressures the proportion is about the same. 

119. Results of Trials : Condensing Engines. A great 
number of good experiments on condensing engines have been 
published : we must be content to give brief references only to a 

Taking single-cylinder engines first, Mr Mair-Rumley's tests^ 
of slow steam-jacketed engines, making 20 revolutions per minute 
and working at about 120 horse-power, show that with a pressure 
of 45 lbs. by gauge in the boiler the consumption of steam need 
not exceed 22 lbs. per i. H. p.-hour : in one case he records a con- 
sumption of 21*3 lbs. under these conditions. These figures corre- 
spond to a thermodjmamic efficiency of 0*10. In Mr Hill's tests 
of £Eister Corliss engines the consumption was from 19*4 to 
20*6 lbs. with a boiler pressure of 96 lbs. by gauge. Mr Willans' 
trials of one of his small high speed single-cylinder engines, 

^ Deaoribed in two papers (J. G. Mair) Iftn. Froc, Inst. C, £., Vols. Ixx. and 

E. 11 


working with a condenser, gave 22*2 lbs. with a steam-chest 
pressure of 100 lbs. per square inch above the atmosphere^ 
increasing to 30 lbs. as the pressure was lowered to about 5 lbs. 
per square inch. 

Passing to compound engines, Mr Mair-Rumley*s tests show 
that in three examples of steam-jacketed engines of about 130 
horse-power, making about 25 revolutions per minute, the con- 
sumption of steam with a boiler pressure of 60 to 63 lbs. by gauge 
was 15*5, 151 and 14*8 lbs. per LH.p.-hour. In these cases the 
steam was expanded about 14 times and with this high expansibn 
and slow speed the advantage of the jacket was very conspicuous. 
These figures correspond to a thermodynamic efficiency ranging 
from 014 to 0*15, and in view of the comparatively low pressure 
used must be ranked as exceptionally good results. 

To compare these and other results of condensing tests with 
the performance "theoretically" possible we may take 100"* F. 
as a standard lower limit of temperature ; this is in &ct about the 
usual temperature at which condensation takes place, and it is 
convenient to have a fixed standard. Values of W calculated by 
equation (7) of § 78 on the assumption that this is the lower 
limit are given for various absolute initial pressures in Table X. 
They will be found useful in comparing the actual with the 
ideal performances of condensing engines. 

In the best of the experimental results which have just been 
quoted the absolute boiler pressure was 76 lbs. per square inch, for 
which TF is 274. The work actually done per lb. of steam was 


— j-Q or 172 thermal units, which is not quite 63 per cent, of TT. 

It should be noticed that this is a distinctly smaller fraction of the 
"theoretical" work than is realised in the best non-condensing 
trials. This, indeed, is a general characteristic of the performance 
of condensing engines : it rarely reaches even 60 per cent, of TT, 
whereas 75 per cent, of W has been reached in non-condensing 
trials. The condensing steam-engine is less able to take full 
advantage of the lower part of its temperature range, for there is 
a greater difficulty in making the expansion approximately com- 
plete. Further, the greater range of temperature in condensing 
engines augments the prejudicial action of the cylinder walls. 

The next example is a trial by Professor Unwin of a Worth- 
ington " High Duty" pumping engine at West Middlesex Water 



Works* — a compound direct-acting steam-pump with no fly- 
.wheel, steam-jacketed, and making about 17 double strokes per 
minute. Two testa were made in which the absolute boiler 
pressure was 90 and 76 lbs. respectively, the indicated horse-power 
being 296 and 256. The total consumption of steam was 17*4 
and 17*7 lbs. per indicated horse-power-hour. For these pressures 
the values of W are 285 and 273^. The fraction of W actually 
obtained was 51 and 53 per cent. The thermodynamic efficiency 
was 013. 

Table X. Work theoretically obtainable from one lb, of steam, toith 
complete adiaibatic expwnsion, assuming the lower limit of temperor 
ture to be 100' Fah, 

Absolute piesanre 


Absolute pressure 


of supply 
lbs. per sq. inch. 

Thermal Units. 

of supply 
lbs. per sq. inch. 

Thermal Units. 












31 5i 






















































Tests of a compound pumping engine of 250 horse-power 
(Leavitt) at the Boston Main Drainage Works', making 13 revo- 
lutions per minute, with an absolute boiler pressure of 114 lbs. 

1 Engineering, Deo. 1888. 

' Bo$Um Soc. Civ, Eng, 1885 or Peabody's Thermodynamict of the Steam-Engine^ 
p. 298. 



per Bq. inch, and steam-jacketed, showed a consumption of 13'9 lbs, 
of steam per indicated horse-power-hour in one trial and 14'2 lbs. 
in another. Taking 14*05 as a mean result, the amount of work 
got for 1 lb. of steam was 181 thermal units. This is 60 per cent* 
of W. The thermodynamic efficiency is 016. The consumption 
of coal was measured in the two trials and was found to be at the 
rate of 1*33 and 1*35 lbs. per indicated horse-power-hour — ^figures 
which show that the performance -of the boiler was on the same 
high level with that of the engine. 

An important contribution to this subject will be found in 
the Reports of Marine Engine Trials made by a research com- 
mittee of the Institution of Mechanical Engineers under the 
chairmanship of Professor Kennedy^ These tests deal with large 
engines of modem construction and include several examples of 
the triple-expansion type. The performances are not equally 
good in all cases : the best of those recorded up to 1892 was made 
in a trial of the triple engines of the "Zona," of 650 h.p. The 
high-pressure cylinder only was jacketed. The absolute boiler 
pressure was 180 lbs. per sq. inch. It was found that 13'35 lbs. of 
steam and 1*46 lbs. of coal were used per indicated horse-power- 
hour. The work done per lb. of steam was therefore equivalent 
to 191 thermal units, which is 58 per cent of TF. The thermo- 
dynamic efficiency of this performance is nearly 0*17. 

Professor Osborne Reynolds has published an account and 
discussion of trials made with the experimental triple-expansion 
engine of the Whitworth Engineering Laboratory at Owens College, 
which jdelded some remarkably good results*. With steam in all 
the jackets, a boiler pressure (absolute) of 207 lbs. per sq. inch, 
these engines, running at about 300 revolutions per minute and 
indicating 72 horse-power, took 12*68 lbs. of steam per indicated 
horse-power-hour, and the consumption of coal was 1*33 lbs. This 
makes the work done per lb. of steam equal to 201 thermal units, 
which is 59 per cent, of W. The thermodynamic efficiency 
is 0'18. Small as these engines are a better performance has 
hardly ever been recorded. 

Reference has already been made to the important series of 

^ Proe, Jrut. Mech, Eng, from 1889. The trials of the ** lona " were reported in 
April, 1891. For a summary of results of that and other trials see the Beport of 
May, 1892. 

« Miiu Proe, Jnst, C. E., Dec. 1889. 


trials made by Willans, which gave results ahnost equal to this last. 
In several of his triple-expansion condensing trials the recorded 
consumption of steam is below 13 lbs. and in one it is only 
12*74 lbs. per indicated horse-power-hour. This was with an 
absolute steam-chest pressure of 185 lbs. per square inch (the 
boiler temperature, which must of course have been somewhat 
higher, is not stated). The engine made 375 revolutions per 
minute and had no jackets. Each pound of steam gave 200 
thermal units of work, and if we take the steam-chest pressure 
as the upper limit in reckoning W, this is quite 60 per cent, 
of the "theoretically" possible quantity. If we were to take 
the boiler pressure, as has been done in other cases, the realised 
percentage of W would still be close on 60. The thermodynamic 
eflSciency is very nearly 0*18. 

Throughout the two-cylinder compound condensing trials made 
by Willans the work done per lb. of steam was generally, at the 
highest speeds, from 50 to 55 per cent, of W. The least con- 
sumption of steam in them was 14*26 lbs. per indicated horse- 
power-hour, which was reached when the steam-chest pressure 
was approximately 175 lbs. Hence it corresponds to 54 per cent, 
of W. 

Mr Donkin cites a number of exceptionally good results 
obtained in trials of the " Sulzer" engine by Professor Schroter 
and others\ Professor Schroter's trials show that a triple- 
expansion engine of about 200 horse-power, using steam with an 
absolute pressure of 171 lbs. per sq. inch, with jackets, consumed 
only 12*2 lbs. per indicated horse-power-hour exclusive of water 
condensed in the steam-pipe, and 12*56 lbs. when this condensed 
water was included. Taking the former figure the yield from each 
pound of steam was the mechanical equivalent of 208 thennal 
units, and since W was 326, this amounts to nearly 64 per cent., 
a proportion which is unusually large for a condensing trial. The 
thermodynamic eflSciency, whether account be taken of the water 
condensed in the steam-pipe or not, is over 0*19. 

In another trial by Professor SchrSter of a triple-expansion 
Sulzer engine of 600 horse-power, the consumption of steam was 
12*65 lbs. per indicated horse-power-hour, the absolute pressure 
of the steam being 160 lbs. per sq. inch. In two-cylinder 

^ The Engineer and Engineering, Jan. 15, 1892. 



compound engines of the same type th6 consumption is stated to 
be 14*3 lbs. per indicated horse-power-hour, as the mean of ten 
experiments made at pressures generally ranging from 100 to 
105 lbs. (absolute). A single-cylinder Sulzer engine of 300 horse- 
power tested by Professor Linde consumed 19 lbs. of steam per 
horse-power-hour when the boiler pressure was 106 lbs. (absolute). 
This implies a jdeld equal to 45 per cent, of W and an efficiency 
of 012. 

Table XL is a summary of the more important results which 
have been quoted for condensing-engine triala 

Tablb XI. Eemlts of Trials of Condensing Engines. 

Type of EDgihe. 

Absolute boiler 

lbs. per sq. inch. 

Steam used 

per hour 

per I. H. P. 


age of W 


Single-cyl. beam pmhping 
! engine (Mair-Ramley . 





Single-cyl. Corliss engine 






Single-cyl. Sulzer engine 





' Two-cyl. componnd beam 
pnmping engme (Mair- 





Two-cyl. compound Worth- 
ington "High Duty" 
pumping engine (Unwin). 







Two-cyl. componnd pump- 
ing engine (Leavitt). 
(Mean of two trials.) 





Two-cyl. compound high- 

180 (about) 




Triple marine engine of 
S. S. "lona" (Kennedy). 





Triple experimental engine 





Triple high-speed single- 
acting engine (Willans). 

190 (about) 




Triple Sulzer engine 






120. Mechanical Efficiency of the Engine. All these 
figures refer to the indicated horse-power, — to the work done 
upon the piston by the steam. But as the object of a steam- 
engine is to drive some other machine or machines it is important 
to recognise the distinction between the indicated work done in 
the cylinder and that quantity of work (always smaller) which the 
engine does against external resistance. Say that the engine is 
set to work against a brake, the " brake horse-power " or " eflfective 
horse-power " will be less than the indicated horse-power by an 
amount which represents the expenditure on friction of one kind 
and another in the mechanism of the engine itself. The ratio of 
the one to the other is the mechanical efficiency of the engine* 
In favourable cases the mechanical efficiency is about 0*85; in 
other words, some 15 per cent, of the indicated work is ineffective, 
being spent on friction within the engine. Occasionally the 
mechanical efficiency may approach 0*9 ; in general, however, it is 
a good deal less. When a steam-engine is directly employed to 
drive a dynamo, the comparison is often made between the elec- 
trical output and the indicated work : in that case the efficiency of 
the djmamo is of course involved as well as that of the engine as a 
mechanism. Similarly in dealing with pumping-engines, the 
comparison is usually made between the indicated work and the 
work usefully applied by the pump — this latter being determined 
by the volume and pressure of the fluid delivered. Here again 
the mechanical efficiency of the pump and of the engine are both 

In the Worthington engine trials referred to above the output 
of the pump represented 84 to 85 per cent, of the indicated work 
done by the steam. In the Leavitt trials also it was 84 per cent. 
In Professor Reynolds' tests, when the engine was loaded by 
means of brakes, the brake horse-power was 82 per cent, of the 
indicated power in the most favourable instances. 

With a given engine running at a given speed the work 
expended in driving the engine itself is usually a nearly constant 
quantity, whether much or little effective work is being taken off. 
Hence the mechanical efficiency is reduced when the load on the 
engine is lightened. We shall have occasion in the next chapter 
to revert to this subject and to describe means of finding and 
of stating the loss which the energy suffers in its transmission 
through the mechanism. 


121. Cunre of Expansion to be assumed in estimat- 
ing the probable indicated horse-power of steam-engines. 

Largely as the exchanges of heat between the working sub- 
stance and the cylinder affect the consumption of steam, their 
influence on the form of the expansion curve is but slight. In 
practical cases the curve is never very different from a rectangular 
hyperbola. The simple supposition that the pressure during 
expansion varies inversely with the volume will answer suffi- 
ciently well in forming conjectural indicator diagrams for such a 
purpose as the estimation of the probable power to be exerted 
by an engine of given size, when the speed, initial pressure, back- 
pressure and ratio of expansion are assigned. 

If there were no clearance, if the full pressure of supply, pi, 
were maintained during the admission, if the cut-off and release 
were perfectly sharp, if the expansion continued to the very end 
of the stroke, .and if there were a uniform back pressure p^, 
without compression, then the assumption that the curve of 
expansion may be treated as a common hj^erbola would make the 
mean effective pressure equal to 

yi(l + log,r) 

where r is the ratio of expansion, namely the ratio which the 
whole volume of the stroke bears to the volume that is swept 
through up to the point of cut-off The same foi*mula would be 
applicable to compound expansion, r being interpreted as the 
final ratio, if the further condition were satisfied that there should 
be no loss of pressure during the transfer of the steam from one 
cylinder to the next. 

In practice, of course, these conditions are not fulfilled, and the 
general result is to make the actual mean effective pressure p^ 
less, in a proportion which is sometimes stated by the use of a 

coefficient e, thus: 

J j?,(l+log, r ) ) 
Pfn = ei^ ; -P^J- 

The diagram factor, as Professor Unwin* has called 6, is a 
number less than unity, which may be estimated as a matter of 
experience from the results given by other engines of like types, 
working under more or less similar conditions. 

* The Practical Engineer, June 17, 1892. See also remarks by Blr C. H. Wing- 
field, Min, Proc, Inst, C, £., Vol. oxiv. p. 83, and Engineering, Oct. 20, 1893. 



122. The Indicator. In this chapter we have first to 
describe the ordinary process of taking indicator diagrams, whether 
for the purpose of finding the horse-power of an engine or of 
examining the action of the steam ; then, to speak of those further 
measurements that have to be made when the thermodynamic 
efficiency of the engine is under trial, and finally to mention a 
method of finding the brake horse-power which, by comparison 
with the indicated power gives the mechanical efficiency. The 
indicator diagram, apart from its use in determining power, is 
invaluable as an index of what is going on within the cylinder. 
It shows the time and manner of the four events of the stroke, 
namely the admission, cut-off, release and compression, which 
together make up what is called the "distribution" of the steam ; 
it detects faults in the setting or in the working of the valves and 
suggests changes by which the distribution may be improved. 
When the information which it gives is supplemented by a know- 
ledge of how much steam is passing through the cylinder per 
stroke a complete analysis of the action becomes possible ; the 
wetness of the steam at any stage may then be determined, as 
well as the exchanges of heat that take place between the steam 
and the cylinder walls. 

The indicator, invented by Watt and improved by M'Naught 
and by Richards, consists of a small steam cylinder, fitted with a 
piston which slides easily within it and is pressed down by a spiral 
spring of steel wire. The cylinder of the indicator is connected by 
a pipe below this piston to one or other end of the cylinder of the 
engine, so that steam firom the engine cylinder has tree access and 



the piston of the indicator consequently rises and falls in response 
to the fluctuations of pressure which occur in the engine cylinder. 
The indicator piston actuates a pencil, which rises and &lls with it 
and traces the diagram on a sheet of paper fixed to a drum that is 
caused to turn back and forth about its axis through a certain 
angle, in unison with the motion of the engine piston. In 
M'Naught's indicator the pencil was directly attached to the 
indicator piston, in Richards's the pencil is moved by means of 
a system of links so that it copies the motion of the piston on 
a magnified scale. This has the advantage that an equally large 
diagram is drawn with much less movement of the indicator 
piston, and errors which are caused by the piston's inertia are 
consequently reduced. In high-speed engines especially it is 
important to minimize the inertia of the indicator piston and 
the parts connected with it. In Richards's indicator the linkage 
employed to multiply the indicator piston's motion is an arrange- 
ment similar to the parallel motion which was introduced by 
Watt as a means of guiding the piston-rod in beam engines. 
In several recent forms of indicator lighter linkages are adopted, 
and other changes have been made with the object of fitting the 
instrument better for high-speed work One of the best of these 
modified forms of Richards's indicator is that made by the Crosby 
Company, which is shown in figs, 47 and 47 a. The pressure of 

Fio. 47. Crosby Indicator. 


indicator and the point from which motion is taken — ^as will 
generally be the case in Jarge engines— cord should be used only 
at places where flexibiljity is required and stout wire should as far 
as possible be substijrdted. Even in comparatively small engines 
wire may be used ,with advantaged Of all the errors to which in- 
dicator diagrams^iire liable perhaps none are so often neglected as 
those that con^e from the stretclung of long driving cords'. 

124 Directions for taking Indicator Diagrams. In 

taking indicator diagrams the following practical hints may be 
found useful: — Before attaching the indicator to the engine, see 
that the indicator is clean and in good order; that the piston 
moves very freely; that the joints of the lever and links are 
oiled with fine oil and are suflBiciently slack to avoid friction, 
but not so slack as to allow the pencil to shake ; that the pencil 
point is sharp, and that it is adjusted to press lightly upon the 
paper drum ; and that the paper drum turns freely without shaking. 
The spindle on which the drum turns needs oil now and then. 

Select a spring appropriate to the pressure within the cylinder 
and to the speed of the engine. With the Crosby indicator the 
diagram should not be more than 1| inches high; thus a 50 
spring should not be used if the range of pressure to be indicated 
exceeds 87 lbs. per sq. in. When the engine runs fast it is neces- 
sary to use a still stiflfer spring, to prevent the diagram from 
showing an inconvenient amount of oscillation. If large oscilla- 
tions occur the process of smoothing the diagram by sketching 
a line midway between the crests and hollows is unsatisfectory, 
and a new diagram must be taken with a sti£fer spring. 

In putting a spring in and screwing the parts together, try 
whether there is any backlash or shake between the spring and 
the indicator's piston. If there is any it is to be taken up (in 
the Crosby instrument) by means of the set screw under the 

Screw the indicator cock to the pipe on the engine cylinder, 
and couple up the indicator, taking care to tighten up the coupling 

^ See for example the devioe used by Prof. 0. Reynolds on the experimental 
engine at Owens College, by which the length of the cord is reduced to a few inches 
(Min, Proc. Inst. C. E., Vol. xc, 1889). 

^ For a discussion and experimental investigation of the errors of the indicator, 
see papers by Prof. 0. Beynolds and Mr H. W. Brightmore (Min, Proc, Inst C,E,, 
Vol. Ixxziii., 1886). 


collar in such a position that it leaves the handle of the cock £ree 
to turn. See that the cord from the drum has a clear course to 
the oscillating lever, and that its mean position during the oscil- 
lation is about perpendicular to the lever. Adjust the length of 
the cord and the amount of its motion so that when the cord is in 
gear the drum turns backwards and forwards without coming up 
against a stop at either end of its travel. If it touches one stop 
or the other the cord is too long or too short : if it touches both 
stops the travel of the drum is too great and a point nearer the 
fulcrum of the oscillating lever must be taken for the attachment 
of the driving cord. 

Do not keep the indicator drum moving except while diagrams 
are being taken. Stop the drum by disconnecting the cord from 
the oscillating lever before attempting to put a paper on the drum. 
In putting on the paper see that it is taut and clear of wrinkles, 
and fold down the projecting edges so that they may not touch 
the lever which carries the marking pencil. 

Turn on steam to the indicator for a minute or so before taking 
the diagram. Then press the pencil lightly on the paper, keeping 
it on long enough to complete a single diagram. Withdraw the 
pencil. Shut the cock leading to one end of the cylinder and 
open the cock from the other end (if pipes from both ends come to 
the same indicator). Touch the pencil to the paper again to take 
the other diagram. Withdraw it and shut the indicator cock. 
Touch the pencil again to the paper to draw the atmospheric line. 
Stop the drum by disconnecting the cord. Remove the paper 
and mark the diagrams to show which end of the cylinder each 
refers to. Note the scale number of the spring, and the speed of 
the engine, with the date and hour and any other particulars that 
may be wanted. 

126. Calculation of the Indicated Horse-Power. By 

measuring the mean height of the diagram between the top and 
bottom lines we find the mean effective pressure, which when 
multiplied by the area of the piston and the length of the stroke 
gives the work done per stroke. 

The mean height of the diagram is most accurately found by 
measuring the area of the diagram with a planimeter or otherwise 
and dividing that area by the length of the base, namely the 
distance between lines drawn perpendicular to the atmospheric 


line and touching the diagram at its extremities. More usually 
the mean height is found by dividing the base into ten or twelve 
equal parts, drawing a perpendicular to the atmospheric line 
through the middle of each of these parts, measuring the lengths 
of these perpendiculars between the top and bottom lines and 
taking the mean of these lengths. The lengths of these per- 
pendiculars are most conveniently measured by applying to each 
line in succession the edge of a scale graduated in inches and 
tenths of an inch : with a little practice it is easy to estimate to 
hundredths of an inch. The mean height in inches is multiplied 
by the scale number of the spring to find the mean effective 
pressure in lbs. per square inch. The mean effective pressure 
for the other side of the piston is found from the other diagram 
in the same way. Calling these mean effective pressures pm and 
Pm, in lbs. per square inch, and the net areas of the corresponding 
sides of the piston a and a' in square inches, and the length of 
the stroke I in feet, the work done by the steam per revolution is 

in foot-pounds. 

The work done per minute is 

n being the number of revolutions per minute ; and the indicated 

^„^_' ^l{Pm(i^Pma') 
' 33000 

In general a and a' are nearly equal. The mean of them may 
then be taken and multiplied by pm + Pm, as a substitute for the 
quantity within brackets. And it is convenient when many dia- 
grams are to be worked out for one engine to express the quantity 

9 ^^00 ^ * single constant factor which has only to be multi- 
plied by n(pm+Pm) to find the indicated power. 

In place of the ordinary indicator an apparatus is occasionally 
used which integrates the two coordinates which it is the .business 
of the indicator diagram to represent, and exhibits the power 
developed from stroke to stroke by the progressive movement of 
an index round a dial. 

126. Examples of Indicator Diagrams. Fig. 49 shows a 
pair of indicator diagrams taken from a Corliss condensing engine,. 
E. 12 



in which after a very early cut-off the whole expansion is performed 
in a single cylinder. In these and subsequent diagrams lines are 

Fio. 49. Indicator diagrams from Corliss Engine. 

added at either end which show the amounts of the respective 
clearances and as base line the line of absolute vacuum is drawn, 
the distance of which below the atmospheric line is determined 
by reading the barometer. The numbers are pressures in lbs. per 
square inch above the atmosphere. Inspection of the diagram 
shows that the distribution of steam is very symmetrical as regards 
the two ends of the cylinder ; also that the amount of compression 
might be increased with advantage. If an adiabatic curve be 
drawn through the point of cut-off (assuming a reasonable percent- 
age of wetness) it will be found that the actual curve of expansion 
at' first lies below the adiabatic curve but afterwards rises above it 

Atmospheric Lin". 

- so 

- 40 

-10 __^______ 

Fio. 50. Indieator diagram from compoand engine: High-pressure <7Under. 

Fio. 51. Low-pressure cylinder. 



in consequence of the re-evaporation of the condensed water 
{§ 105). Figs. 50 and 51 show a set of diagrams taken from a 
small compound engine using slide valves. Fig. 50 is the high- 
pressure pair of diagrams and fig. 51 is the low-pressure pair. In 
the former the cut-off is a little sharper on one side than on the 
other, but the distribution is on the whole symmetrical and good. 
The points of release and compression are well marked, showing 
that there is a free exhaust. Other examples of compound 
diagrams will be given later. 

Indicator diagrams are often taken for the purpose of testing 
the setting of the valves although the circumstances may be such 
that the engine is not doing external work. Fig. 52, for instance, 
is a pair of diagrams taken from a Corliss engine when first erected 

Fio. 52. Indicator diagrams taken to examine the action of the valves. 

by the makers without having the condenser in action and with 
no external load. The exhaust is into the atmosphere, and as 
expansion has made the pressure in the cylinder less than that of 
the atmosphere the pressure rises at release (c, c' in the figure). 
This produces a loop on the diagram representing negative work : 
the excess of the positive over the negative portion represents the 
net amount of work which is done by the steam in overcoming 
the friction of the engine. 

127. Thermodynamic Tests. Mea4rarement of the 
Supply of Steam by means of the Feed. When engine trials 
are to serve as tests of thermodynamic performance, either the heat 
supplied or the heat rejected has to be measured, for comparison 
with the work done. Measurements of the supply of heat are most 
usual. Sometimes, however, this method of testing may be im- 
practicable and a test by means of the rejected heat may be easy. 



In any case a measurement of the rejected heat furnishes a 
valuable check on the accuracy of the other method, and the 
most satis£Eictory trials are made by measuring the heat supplied 
as well as the heat rejected; this allows a species of balance- 
sheet to be drawn up in which the heat given to the engine 
is more or less completely accounted for. 

To determine the supply of heat the quantity of steam used by 
the engine is measured. Except when the engine has a surface- 
condenser, this has to be done by measuring the amount of feed- 
water that is required to keep the level of water in the boiler 
constant during a prolonged run. A somewhat long run is 
necessary in a trial of this kind because the level of water in the 
boiler cannot be read very exactly and the whole consumption of 
feed-water must be so great that any error due to this cause 
will become negligible. With an ordinary Cornish or Lancashire 
boiler a run of six or eight hours may be desirable and even 
essential if an accurate result is to be got : on the other hand 
if the engine is getting its steam from a small tubular boiler 
workiDg hard under forced draught, the evaporation may be so 
rapid that a single hour will suffice. Cai*e should be taken to 
have all the conditions of the experiment as closely as possible 
the same at the end as at the beginning of the trial: if for 
instance the feed-pump is working at the beginning it should be 
working at the end at the same rate, and the pressure in the 
boiler should be the same. In these circumstances the quantity 
of water in the boiler, for a given reading in the gauge-glass, 
may be taken to be the same at the end as at the beginning 
of the run, and the quantity of feed- water that has been supplied 
in the interval is therefore equal to the quantity of steam (dry 
or wet) that has left the boiler. If there has been no leakage and 
no blowing oflF at the safety-valve or otherwise, this quantity of 
steam has been delivered to the. engine. 

To measure the feed-water a very convenient plan is to have 
two tanks, one a small tank (A fig. 53) set above the other (B) so 
that it may drain into B. The weight of water contained by A 
when full must be accurately known, and it should be furnished 
with a gauge-glass C to let fractions of the whole contents be 
read. B must have a float or a point gauge D or other mark in 
it to indicate when the water reaches some one standard level. 
The feed-pump draws water from J? by the pipe £; fresh water 



can be run into A at pleasure from the supply pipe F, and there 
is a stop-cock between A and B, At the beginning of the 
test let it be seen that the water m B ia a.t the standard level 
and that the stop-cock betweer// 
the tanks is shut. Supply water 
during the test by completely fill- 
ing A as often as may be necessary, 
letting its contents drain com- 
pletely into B each time and not- 
ing the hour and minute at which 
each fill of ^ is emptied into B. 
At the end of the trial, after fill- 
ing A for the last time let just 
enough of its contents pass into B 
to bring the level of water in B 
up to the standard, and read on 
the gauge-glass of A the fraction 

which completes the whole supply, p^^ 53 Arrangement of tanks for 
In a long run it is useful to check measuring feed-water, 

the work by dividing the whole period into two or more parts, in 
each of which the supply of feed-water is separately noted. The 
boiler pressure, the speed, and all other conditions of working 
must of course be kept as nearly uniform as may be throughout 
and should all be noted at regular intervals during the trial. 

The engine should work for some time under the prescribed 
conditions as to speed, pressure, and load before the period of the test 
begins, in order that it may get thoroughly warmed up and that a 
uniform action may be established. During the trial indicator 
diagrams are taken from time to time and the times are noted. 
Where there is a mechanical counter the whole number of revolu- 
tions made during the period of trial is found by reading the 
counter at the beginning and at the end. 

128. Measurement of the Supply of Steam by means of 
the Condensed Water. In engines which are fitted with a surface 
condenser the amount of steam passing through the engine in a 
given time is readily determined by weighing the condensed water 
discharged from the air-pump. An important advantage of this 
method is that a satisfactory trial of the engine can be made in 
much less time than is necessary when the steam used is to be 



determined from the feed-water. Provided the engine has been 
running long enough for the action to become uniform before the- 
trial begins, the air-pump discharge need not be collected during^ 
more than ten or fifteen minutes, and thus a series of distinct trials 
under different conditions can be made in a single day. 




129. Measurement of Jacket steam. If the engine ha» 
jackets the water condensed in them must be measured in addition 
to the water discharged by the air-pump; and even when the whole 
supply of steam is inferred from the feed it may be desirable to 
determine separately the amount that is used in the jackets. This is 
done by draining them into a tank or tanks so that the condensed 
water may be weighed. The water must escape freely enough to 
prevent its accumulating in the jacket 
and yet not so freely as to let steam 
blow through. This is readily secured 
by means of one or other of the devices 
shown in fig. 54. A gauge-glass is in- 
serted in the jacket drain, or is fitted to 
the drain as in the left-hand figure, with 
a throttle valve below it. By adjusting 
this valve the escape of the condensed 
water can be regulated so that the 
surface of the water will show itself in 
the glass at a constant height; the 
water is then passing off just as fast 
as it IB condensed. To prevent evapora- 
tion of the discharged water the con- 
tinuation of the drain may pass in the 
form of a bend or worm through a 
tank of cold water so that the jacket 
water may be cooled before it reaches the vessel in which it 
is to be measured*. 

Fia. 54. Gauge on Jacket 

130. Comparison of Feed-water with Discharged 
Water. In many trials the quantity of steam used by the 
engine is measured by both of the means that have been de- 

1 This device was shown to the author by Mr Bryan Donkin, who had nsed 
it in some of his engine tests. It is also used in the Barrus Calorimeter de> 
scribed below (§ 182). 


scribed, namely by finding on the one hand how much feed is 
supplied to the boiler, and on the other hand how much is 
discharged by the air-pump and the jacket drains. In most 
cases some discrepancy is observed: the feed- water may be as 
much as five per cent, more than the discharged water. This 
apparent loss of substance is. due in part to water-vapour 
being discharged from the air-pump without being included in 
the measurement, but it is mainly due to leakage. Steam may 
escape at joints in small quantities showing little trace of its 
presence, and there is often some leakage within the boiler, 
as for instance at the ends of the tubes into the firebox in a 
boiler of the locomotive or the marine tjrpe. In most cases the 
measurement of the water discharged by an engine gives a fairer 
test of its performance than is given by measuring the feed. 
Should a serious discrepancy between the two quantities be found 
its causes are of course to be searched for and remedied. 

131. Estimation of Heat supplied. Measurement of 
Dryness of the Steam by the ^^BarreP' Calorimeter. Know- 
ing the amounts of steam supplied to the cylinder and jackets we 
may go on to calculate the amount of heat which the working sub- 
stance takes up. In the absence of information as to the propor- 
tion of water in the steam as supplied to the engine the assump- 
tion that the steam is dry is the only safe one, though this may 
do some injustice to the engine by over-estimating the supply 
of heat. When the dryness q is known the heat supplied per lb. is 

qL + h — ho, 
Ao being the heat already present in the feed-water. Direct 
measurement of q is diflBcult mainly because it is difficult to secure 
that the steam used in a test of g is of the same quality as that 
which is delivered to the engine. One method is to blow steam 
jfrom the boiler into a barrel or other vessel containing water, 
allowing the steam to be condensed, and noting the amounts by 
which (1) the temperature and (2) the weight of the contents 
have become increased after a suitable time. The former shows 
how much heat has been given up in condeusing the steam that 
is blown in ; the latter shows what the quantity of that steam is. 
Let the temperature rise from ^ to t^ while the weight increases 
from TTi to TFa. Then q is found from the equation 
{W,- W,)(qL + h--h,)^ F,(A,-U 


where h^ and A, refer to the temperatures ^ and ^, and h and L 
refer to the condition of the steam as supplied. This is subject to 
corrections (1) for loss of heat by radiation and (2) for the thermal 
capacity of the barrel itself Accurate results are not easily got on 
account of the large error which is introduced by any inexactness 
in the measurement of the weight. 

132. Barms Calorimeter. A better form of calorimeter has 
been devised by Mr Barrus which also determines the wetness of 
steam by measuring the heat given out during its condensation, but 
the condensed steam is not allowed to mix with the condensing water. 
The steam to be examined flows into a pipe which passes through 
a vessel of water and so forms a surface-condenser. A steady 
circulation of water is kept up in the vessel, cold water flowing in 
and passing off after having been warmed by the condensation of 
steam within the pipe. The temperatures ti and U of the water 
at the inlet and outlet respectively are noted. The water formed 
by condensation in the pipe is weighed after allowing it to escape 
through a stop-cock furnished with a gauge-glass as in fig. 54 
(§ 129) and its temperature i^ is noted. The quantity of cooling 
water which passes through the vessel in a given time has also 
to be weighed. Before an observation is made the apparatus is 
kept running long enough to let the temperatures all take steady 
valuea Then, if W be the quantity of cooling water which passes 
while the quantity w is condensed, 


subject to a small correction for radiation as before, the amount of 
which can be determined by noting the rate at which the calori- 
meter cools when it stands full of water at temperatures inter- 
mediate between ti and t^ 

133. Peabody Throttling Calorimeter. Professor Peabody ^ 
describes a simple calorimeter of his own design which acts by 
throttling the wet steam until it becomes slightly superheated 
(see § 76). The steam passes through an adjustable throttle-valve 
Ay fig. 55, into a chamber B lagged with non-conducting material, 
in which its temperature and its pressure are observed by ther- 
mometer C and gauge D. From this it escapes through another 

^ Thermodynamics of the Steam-Engine, p. 237. 



adjustable valve E to the atmosphere or to a condenser. The 
valves are adjusted until the steam in the chamber is seen to 
be slightly superheated, by comparing the observed temperature 
with the temperature which, in 
saturated steam, would correspond 
to the observed pressure. The 
amount of superheating, and the 
drop in pressure which has caused 
it are noted. Let pi be the pres- 
sure in the chamber and i^ the 
temperature which saturated steam 
at that pressure would have, and 
let t^ be the actual temperature. 

grL +A = Zi + Ai + a:(^'-^), 
where k is the specific heat of 
steam when superheated under 
constant pressure, a quantity which 
may be assumed to have a value 
nearly equal to 0*48. 

It is only when the steam is 
nearly dry to begin with that it 
can be superheated or even dried by throttling. In using the 
apparatus there is no need to make t^ greater than ^ by more 
than a trifling amount — just enough to ensure that the steam in 
the chamber is perfectly dry. Even then however the limit of 
wetness beyond which the throttling calorimeter cannot be used is 
not high. With steam at 100 lbs. pressure, for instance, only 
4 per cent, of moisture can be removed by throttling if the pressure 
in the chamber is as low as that of the atmosphere: but if a 
condenser is available the pressure in the chamber may be reduced 
hx enough to deal with about 6 per cent. 

134. Measurement of Heat rejected by an Engine. 

The rejected heat is measured by observing the quantity of the 
condensing water and the amount by which its temperature rises as 
it passes through the condenser. With small engines the quantity 
may be found by direct weighing or measuring in a large tank, 
or by the use of a pair of measuring tanks arranged so that one 
filb while the other empties. But in general the quantity of 

Fia. 55. Throttling 




condensing water is too great to be easily treated in this way, and 
it has rather to be gauged as a stream, by observing the head under 
which it flows through an orifice of known size, or over a weir* 
This gauging is generally done after the water leaves the condenser, 
in which case, if the condenser is of the injection tjrpe the quantity 
that is measured is the sum of the cooling water and the condensed 
steam, and the amount of the cooling water alone can be inferred 
by deducting firom the whole a measured or estimated allowance 
to represent the feed. 

When the stream to be gauged is large an open weir with a 
rectangular or Y-shaped notch will be found most convenient: 
but for small streams a submerged circular orifice has the advantage 
that the accuracy of the result is less affected by any small error 
that may be made in measuring the hecul. The steam to be gauged 
enters at A (fig. 56) a box containing baffle plates and perforated 








• • 








• • 


( • 



• • 


• • 








- • 

• • 









Fio. 56. Weir box with dzcnlar orifice. 

diaphragms (sheets of perforated zinc or gauze will do well) which 
reduce it to stillness before it reaches the orifice JS. This is a cir- 
cular hole in a fiat plate, and is bevelled to a sharp edge with the 
bevel outside. The head of water in the chamber close to the orifice 
is to be observed by means of a float and scale which are not shown 
in the diagram. If h is the head in feet, measured firom the sur- 
fiwje to the centre of the hole, and 8 is the area of the hole in 
square feet, the discharge Q in cubic feet per second is given 

by the formula Q=^C8's/2gh, 

where c is a " coefficient of discharge " the ordinary value of which 
for a circular hole in a large flat sur£a.ce is 0*62, when the head is 


sufficient to bring the surface of water to a considerable height 
above the hole\ 

135. Example of an Engine Trial. To illustrate the re- 
duction of the observations and the comparison of the heat 
supplied with the heat rejected and the work done we may take 
the data of a test by Mr Mair-Rumley, from one of the papers 
which were alluded to in last chapter. The engine under trial 
was a compound beam-engine with steam-jackets and with a jet- 
condenser. The cylinders were 21 and 36 inches in diameter and 
the stroke of each piston was 5^ feet. The feed-water was 
measured during a period of 6 hours and the air-pump discharge 
was gauged by means of a weir. The following are the data of 
the trial: — 

Pressure in boiler, 76 lbs. per sq. in., absolute (for which 

i = 898and'A=278). 
Duration of trial, 6 hours. 
Revolutions, 8632, or 24*0 per min. 
Indicated horse-power, 127*4. 
Feed-water, 12032 lbs. 
Air-pump discharge, 1226 lbs. per min. 
Water drained from jackets, 1605 lbs. 
Dryness of steam as supplied, 096. 
Temperature of feed, to = 59° Fah. 

„ „ injection ^ = 50° Fah. 

„ „ air-pump discharge, <a = 73*4° Fah. 

These give the following results : — 

Total feed per revolution = 1*394 lbs. 

Jacket feed per revolution = 0*186 lbs. 
Cylinder feed per revolution = 1*208 lbs. 
Injection water per revolution = ^^ — 1*208 = 49*9 lbs. 

^ When an open rectangular notch with sharp edges in a vertical plate is used 
for a weir, h is to be measured from the bottom of the notch to the free level of the 
Borface, at a distance far enough back to give practically still water : then 

where h is the breadth of the notch. 

With a triangular notch out so that the breadth is twice the depth Q=s2'5ihi, 
where A is the depth of the bottom of the notch below the still- water surface level. 
For the justification of these formulas reference must be made to books on hydraulics 
or to papers by J. Thomson, Rep. Brit. Auoc, 1858, 1861, and 1876, p. 243. 


Heat taken in by the working substance per revolution 
= l-394(3Z+A-Ao) 

= 1-394 (0-96 X 898 + 278 - 27) = 1394 x 1113 
= 1551 thermal units. 

Heat converted into work per revolution 
127-4 X 42-42^ 


= 225 thermal units. 

The whole heat rejected per revolution should therefore be 1326 
thermal units. 

That part of the working substance which is cylinder feed 
rejects heat first and chiefly to the injection water, and secondly 
by becoming itself cooled from ^ the temperature of the air-pump 
discharge to to the temperature at which it returns to the boiler. 
The heat it rejects per revolution in these two ways is therefore 

49-9 (<a - ^) + 1-208 (^a - to\ 

or 49-9 X 23-4 -h 1*208 x 144 = 1184 thermal units. 

That part of the substance which is jacket steam rejects heat 
by becoming cooled from the temperature at which it is condensed 
in the jacket to the temperature at which it is returned to the 
boiler. In the present case the jackets drained into the hot-well 
and the temperature therefore fell to 59°, the temperature of the 
feed. The heat rejected in this way per revolution was 

0-186 (A - Ao) = 0186 (278 - 27) = 47 thermal units. 

Adding these we have 1231 units of rejected heat. A balance 
of 96 units remains to be accounted for. It is made up partly of 
heat carried away by the air and vapour of the air-pump dis- 
charge, partly of losses through radiation from the engine and 
pipes, and partly of heat lost in whatever steam escapes by 
leakage. In the example cited the loss by radiation was estimated 
to amount to 45 units " ; allowing for this the discrepancy between 
the two sides of the account is reduced to 50 units or only about 
3 per cent, of the whole supply. 

^ 42*42 is the thermal equivalent of 1 horse-power acting for 1 minnte, namely 
mi^ thermal units. 

' The loss by radiation is approximately estimated by letting the engine stand 
still with the jackets and steam-chest full of steam and noting the amount that is 
condensed in a given time. 


The consumption of steam per indicated horse-power-hour, 
calculated fix>m the whole amount of the feed is 

12032 ,.^„ 
or 15-7 lbs. 

127-4 X 6 
This makes the indicated work done per lb. of steam equivalent to 

33000x60 ,^o^, , V. 

-ir=rr — =^77; OF 162 thermal units. 
778 X 15-7 

In considering the efficiency of a cycle as a whole we should in 
strictness deduct from this the net amount of work which has to 
be expended in returning the condensed steam from the condenser 
to the boiler or say 0*017 x 76 x 144 foot-lbs. per lb. As this is 
the equivalent of only 0'24 thermal units per lb. the correction is 
unimportant. Since the heat taken in per lb. is 1113 units the 
efficiency of the cycle is 0145 \ 

136. Wetness of the steam during expansion. In § 105, 
Chapter V., it was explained how to find the proportion of water 
present in the cylinder at any stage of the expansion and to 
represent the results of this calculation graphically by means of 
a ''saturation curve" upon the indicator diagram — namely a curve 
which represents the volume which the steam in the cylinder 
should fill at any pressure if it were dry throughout. To draw 
this curve for either side of the piston we should in strictness 
know how the whole amount of the cylinder feed is shared by 
the two ends of the cylinder — a matter which the test does not 
determine. But in general the action in the two ends is so nearly 
symmetrical that results which are practically correct may be 
obtained by combining the indicator diagrams for the two into a 
mean diagram, taking for clearance the mean of the two actual 
clearances, and taking half the cylinder feed per revolution as the 
quantity of steam that enters the cylinder per stroke. The 
diagram shown in fig. 45, § 105, is in fact a combination diagram 
drawn in this way. To determine the wetness of the steam during 
expansion is an important part of an engine test, and the results 
cannot be better exhibited, so far as this particular is concerned, 
than by showing the saturation curve in its relation to the actual 

^ For farther illustrations of engine trials and the reduction of results reference 
should be made to the excellent examples contained in several of Mr M. Long- 
ridge's Reports as Engineer of the Engine, Boiler, and Employers' Liability Asso- 
ciation from 1S80, 


curve of. pressure and volume. In dealing with compound engines 
a saturation curve may be drawn separately for each cylinder, or 
the diagrams for the several cylinders may be combined into 
one by means of a device which will be described in the next 
chapter (§ 149 below). 

This process of estimating the water present during expansion 
by comparing the saturation volume with the volume actually 
filled by the working substance depends on the assumption that 
the whole quantity of substance does not change from the time 
that cut-off is complete until release begins. Any leakage of 
steam, in or out, through the valve or past the piston will invali- 
date the calculation. 

137. Transfbr of Heat between the Steam and the 
Metal. Him's Analysis. Having determined what proportion 
of the working substance is steam and what is water through- 
out the expansion we may go on to calculate how much heat is 
taken from or given to the walls of the cylinder and piston during 
any stage of its action. This analysis of the transfers of heat, 
introduced by Hirn and developed by his pupils and followers, 
has been pursued at great length in some engine tests \ Only a 
very short account of it need be given here. 

Let m and mf represent the quantities of dry steam and water 
respectively present in the working mixture either during ex- 
pansion or during compression. We may use / to represent the 
internal energy of the whole mixture. Its value at any stage is 

(m + m') h -f mp, 

p having the meaning which was assigned to it in § 60. Taking any 
two points in the curve of expansion (or in the curve of compression) 
let the corresponding two values of / be calculated, say Ii and /,. 
Between these two points a quantity of work is done by the steam 
(or upon it, if the compression stage is being considered) which is 
measured by fPdV, where P and F represent the actual pressure 
and volume of the mixture and the integral is taken between 
limits corresponding to the two assumed points. Call this quan- 
tity of work TFia. If it happens that W^ = /i - /a the process is 
adiabatic: no heat in that case has been taken from or given 
to the cylinder walls by the working steam between the two pointa 

1 See Dwelshanvers-Bery, ** Etude CalorimStriqiie de la Machine a Vapeur," 
Also Mr Mair-Bnmley's papers already cited^ 


More generally there will be a diflTerence between the work done 
and the change of internal energy, which difference measures the 
quantity of heat that is transferred to or from the walls. Thus 
if we distinguish the four events of admission, cut-ofif, release and 
compression by the suffixes a, 6, c and d respectively, the heat 
taken up from the cylinder walls during expansion is 

Similarly the quantity 

Qda = Wda — {^d — ^a)t 

in which the values of / relate to the substance shut up in the 
clearance space, measures the heat that is taken up during com- 
pression. Wda is negative. This calculation can of course be 
applied to any stage of either process, and thus by applying it 
to a series of short stages a curve showing the inflow or outflow 
of heat can be drawn from point to point of the stroke. 

During culmission the quantity of the mixture is undergoing 
change. The mixture that is shut up in the clearance at the end 
of the back stroke before admission takes place has a certain 
internal energy /». The steam that enters brings with it an 
additional stock of internal energy, Iq, which may be calculated 
provided the dr3mess of the entering steam is known. The work 
done during admission Waf, is determined from the diagram. 
Then the transfer of heat during admission is 

a quantity which is generally negative in actual cases since heat 
is given to the cylinder walls in this part of the action. 

In attempting to apply the same method of calculation to 
determine the heat taken up from the metal during exhaust (Qed) 
we are met by the difficulty that the state as regards wetness in 
which the mixture leaves the cylinder is not known. The value 
of Qcd may however be estimated indirectly as follows. Let Qab, 
Qte and Qoa represent, as before, the transfer of heat from metal to 
steam during admission, expansion and compression respectively, 
let Qr represent the loss by radiation and Qj the additional supply 
of heat which is furnished by condensation of steam in the jacket, 
all reckoned per stroke. Then if the engine is working uniformly 
the gains and losses of heat on the part of the metal must balance, 
and hence Q«i= Qj - Or - Qab-QbcQda. 

This heat Qcd which is taken up from the metal during the 



exhaust is called in the writings of Him and his pupils " le re- 
froidissement au condenseur" and is sometimes spoken of as 
being in a particular sense the measure of the wasteful action of 
the cylinder walls. It should however be borne in mind that the 
transfer of heat between metal and steam does some mischief even 
when the steam is dry at the end of expansion, in which case 
practically no heat is taken up during exhaust. That part of the 
heat abstracted from the steam during admission which is restored 
before release does not appear in Qcd, nevertheless it reduces the 
efficiency because it is taken from the working substance at a high 
temperature and restored at a lower. And this action goes on even 
when the steam is so dry at release that Qcd is sensibly zero. 

As an alternative to the method used by Him, the entropy- 
temperature diagram may be applied to the purpose of tracing the 
heat stored and restored during expansion, in a manner which has 
been sufficiently indicated in Chapter V. (§ 106). 

138. Testa of meohanioal effloienoy. 
Brake Hone-power. In tests of mechanical 
efficiency the engine (unless it be used for 
pumping) is commonly set to work against 
some form of friction brake arranged to serve 
as an absorption dynamometer. No form is 
so simple or so easy of application as a rope 
brake of the type shown in fig. 57. Two, 
three, or more parallel turns of rope with a 
few wood blocks to hold them apart (the num- 
ber of ropes depending on the quantity of power 
that is to be absorbed) are made to clasp 
the fly-wheel in the manner sketched; the 
slack end is attached to a spring balance and 
the other end is loculed with weights, either 
directly, or through a lever if the amount of 
locul is inconveniently great. A little grease 
applied to the surface of the metal makes the 
brake work quietly and steadily. The wheel 
may be kept cool by water ; a wheel with in- 
ternal flanges on the rim, forming an intemal 
channel to which cold water may be supplied, 
is convenient. The resistance is adjusted by 

Measurement of 

Fio. 67. 


varying the amount of the weight Z\. A platform or stop fixed 
a little way below this weight allows the brake to be applied and 
removed by pulling or slacking away the rope by which the spring 
balance is suspended ; by pulling the rope which is shown at the 
top of the figure the weights are lifted off their platform and 
the brake comes into action. When the brake is in action the 
pull T2 indicated by the spring balance is noted from time to 
time. The effective resistance is Ti — T^, and the work done 
against the brake per revolutioD is 2'7rr(Ti — T^) where r is the 
radius measured from the axis of rotation to the middle of the 
rope's thickness. Hence the brake horse-power 

_ 27mr (2\ - T^) 
^•^•■^•"" 33,000 • 

B H -P 

The mechanical eflSciency is the fraction - — ^ — - ; or, without 

reducing to horse-power, it is the ratio of the work done on the 
brake per revolution to the work done by the steam per revolution, 


in the notation of § 125. 

A particularly convenient method of loading the brake is t.o 
anchor the end of it which is to bear the larger pull 2\ to a heavy 
weight resting on a platform balance, care being taken to make 
this weight considerably greater than the greatest value to which 
2\ will rise. The light end may then be loaded by means of a cord 
passing round a pulley overhead and carrying fiwijustable weights. 
When the brake is in action Ti is observed by noting on the scale 
of the platform balance how much apparent weight is lost by the 
heavy mass which forms the anchorage. 

139. Trials of an engine under various amounts of load. 

Although some engines are required to work always under the 
same or nearly the same conditions as to load, more commonly the 
load is liable to variation, and it may be as important to examine 
the performance under light loads as to make trials at full power. 
At electric light stations, for example, much of the work is done 
with a comparatively light load on the engine and the efficiency 
under these conditions is a matter of the greatest moment. To 
E. 13 



be complete a trial should include a series of tests made at 
various grades of output from full power down to the extreme 
when the engine merely drives itself without doing external work. 
The papers by Mr Willans which were referred to in Chapter IV. 
contain many examples of trials which are complete in this sense. 
Such results may be represented graphically by drawing a curve 
in which the ordinates are the number of lbs. of steam consumed 
per horse-power-hour, with the rate of output in horse-power for 

Two curves of this kind are shown in fig. 58, relating to two 
series of tests by Willans of one of his compound high-speed 







r '"'" 


_ ^ 




15 20 25 

Indicated JTorte Power 
Fio. 58. 

single-acting engines, using a condenser^. In one set of trials 
the ratio of expansion was 4*8 and the points through which the 
curve is drawn were determined by testing the consumption 
under various values of the initial steam pressure, ranging from 
136 lbs. per sq. inch (absolute) down to 43 lbs. The other curve 
refers to a similar series of trials in which the ratio of expansion 
was 10. 

Another useful way of showing the performance at all powers 
is to plot the whole quantity of steam consumed per hour in 
relation to the horse-power. Curves of this kind were first used 
by Willans : examples of them are given in fig. 59 relating to the 
same two sets of trials as fig. 58. In each set of trials the 

1 Min. Proe, Jfut. C. JB., Vol. oxiv. 1898. 



adjustment of the power was acccmiplished by varying the initial 
pressure of the steam, the cut-off remaining constant throughout 
the set. Under these conditions Willans found that the curve 
of total steam consumption in relation to power (fig. 59) was 
sensibly a straight line. With variable cut-off and constant 
pressure, on the other hand, it is bent, having a steeper gradient 
at high powers than at low powers. 

The same tjrpes of diagram are useful in representing the 
consumption of steam in relation to brake horse-power, pump 
horse-power, electrical horse-power, etc. They exhibit clearly 
under what condition the maximum of efficiency will be reached, 


















^ ^^ 




15 20 28 80 

Indicated Hone Power 
Fig. 69. 

and also what the performance will be under the less favoumble 
conditions that may have to be submitted to in practice. 

When the Willans' line (fig. 59) is a straight line the whole 
consumption of steam at any load may be regarded as made up of 
two parts — the constant unproductive consumption that takes 
pkce without doing work in the cylinder and a further consumption 
that is simply proportional to the indicated power. The whole 
consumption is equal to 




where i is the number of horse-power and a is the ratio at which 
steam is taken per horse-power after the unproductive supply ah 
has been furnished. 

The same remark holds good in relation to a Willans' line 
drawn with the external or brake horse-power as the base; ab 
then represents the steam that is used in making the engine drive 
itself; and b is what may be called the '^idle work/' a quantity 
which is somewhat greater than the indicated work done in over- 
coming engine friction. 

A comparison of the Willans' lines relating to indicated and 
brake power respectively serves to show how tar the work spent on 
engine friction remains constant at high powers and at low. In 
general it may be expected that this quantity will be greater at 
high powers since the forces at the joints of the mechanism 
become on the whole increased. 



140. Woolf Engines. When the expansion of steam is begun 
in one cylinder and continued in another, the steam may either be 
made to pass directly from one cylinder to the next, or it may pass 
from the first cylinder into an intermediate chamber, called a 
"receiver" from which the second cylinder draws its supply. An 
advantage of the latter plan is that it does not require the reception 
of steam by the second cylinder to be simultaneous with the 
rejection of steam by the first. This allows the cranks to be set 
at any angle, it also allows the distribution of the expansion between 
the two cylinders to be readily adjusted. Chiefly for this reason 
compound engines are now rarely used with immediate transfer 
of steam from one cylinder to the other. 

The original form of compound engine invented by flomblower 
and revived by Woolf had no receiver. Steam passed directly 
from the high to the low pressure cylinder, entering one as fast 
as it was exhausted from the other. This arrangement is possible 
only when the high and low pressure pistons begin and end their 
strokes together, that is to say, when their movements either 
coincide in phase or differ by half a revolution. Engines of the 
" tandem " type satisfy this condition — engines, namely, of which 
the high and low pressure cylinders are in one line, with one 
piston-rod common to both pistons. Engines whose high and low 
pressure cylinders are placed side by side, and act either on the 
same crank or on cranks set at 180'' apart, may also discharge steam 
directly from one to the other cylinder ; the same remark applies 
to beam engines with high and low pressure cylinders standing 
side by side. By a convenient usage which is now pretty general 
the name '' Woolf engine " is restricted to those compound engines 


which discharge steam directly from the high to the low pressure 
cylinder without the use of an intermediate receiver. 

141. Receiver engine. An intermediate receiver becomes 
necessary when the phases of the pistons in a compound engine do 
not agree. With two cranks at right angles, for example, a portion 
of the discharge from the high-pressure cylinder occurs at a time 
when the low-pressure cylinder cannot properly receive steam. 
The receiver is in some cases an independent vessel connected to 
the cylinders by pipes ; very often, however, a sufficient amount of 
receiver volume is i^fforded by the valve casings and the steam- 
pipe which connects the cylinders. The receiver, when it is a 
distinct vessel, is frequently jacketed. 

The use of a receiver is by no means restricted to engines in 
which the " Woolf " system of compound working is impracticable. 
On the contrary, it is fr^uently applied with advantage to beam 
and te^ndem compound engines. Communication need not then be^ 
maintained between the high and low pressure cylinders during the 
whole of the stroke : in such cases admission to the low-pressure 
cylinder is stopped before the stroke is completed; the steam 
sdready admitted is allowed to expand independently; and the 
remainder of the discharge from the high-pressure cylinder is 
compressed into the intermediate receiver. Each cylinder has 
then a definite point of cut-off, and by varying the cut-off in the 
low-pressure cylinder the distribution of work between the two 
cylinders may be adjusted at will. In general it is desirable to 
make both cylinders of a compound engine contribute equal or 
nearly equal quantities of work. If they act on separate cranks 
this has the effect of giving the same value to the mean twisting 
moment for both crahka 

Another adjustment which is sometimes aimed at is to make 
the range of temperature equal in both. In general, when the 
division of work is equal, the parts into which the whole tempera- 
ture range is divided are nearly equal also. 

142. Drop in the Receiver. Oompound diagrams. Where- 
ever a receiver is used, care must be taken that there is no serious 
amount of unresisted expansion into it; in other words, the 
pressure in the receiver should be equal or nearly equal to that 
in the high-pressure cylinder at the moment of release. If the 



receiver pressure is less than this there will be what is termed a 
" drop " in the steam pressure between the high-pressure cylinder 
and the receiver, which will show itself in an indicator diagram 
by a sudden fall at the end of the high-pressure expansion. This 
" drop " is, from the thermodynamic point of view, irreversible, and 
therefore wasteful. It can be avoided, as we shall presently see, 
by selecting a proper point of cut-off in the low-pressure cylinder. 
When there is no " drop " the expansion that occurs in a compound 
engine has precisely the same effect in doing work as the same 
amount of expansion would have in a simple engine, provided the 
law of expansion be the same in both and the waste of energy 
which occurs by the friction of ports and passages in the transfer 
of steam from one to the other cylinder be negligible. The work 
done in either case depends merely on the relation of pressure to 
volume throughout the process: and so long as that relation is 
unchanged it is a matter of indifference whether the expansion be 
performed in one vessel or in more than one. It has, however, 
been explained in Chapter Y. that in general a compound engine 
has a thermodynamic advantage over a simple engine using 
the same pressure and the same expansion, inasmuch as it reduces 
the exchange of heat between the working substance and the 
cylinder walls and so makes the process of expansion more nearly 
adiabatic. The compound engine has also a mechanical advantage 
which is referred to in § 147, below. 

The ultimate ratio of expansion in any compound engine is 
the ratio of the volume of the low-pressure cylinder to the volume 
of steam present in the high-pressure cylinder at the point of cut-off. 

Fxo. 60. Compound Diagrams : Woolf type. 

Fig. 60 illustrates the combined action of the two cylinders in a hypo- 
thetical compound engine of the Woolf type, in which for simplicity 
the effect of clearance is neglected and also the loss of pressure which 
the steam undergoes in transfer frt>m one to the other cylinder. 



ABCD is the indicator diagram of the high-pressure cylinder. 
The exhaust line CD shows a £EJling pressure in consequence of 
the increase of volume which the steam is then undergoing 
through the advance of the low-pressure piston. EFOH is the 
diagram of the low-pressure cylinder and is drawn alongside of 
the other for convenience in the construction which follows. 
It has no point of cut-off; its admission line is the continuous 
curve of expansion EF, at each point of which the pressure is the 
same as at the corresponding point in the high-pressure exhaust 
line CD. At any point K^ the actual volume of the steam is 
KL + MN. By drawing OP equal to KL + MN, so that OP re- 
presents the whole volume, and repeating the same construction at 
other points of the diagram, we may set out the curve QPR, the 
upper part of which is identical with BC, and so complete a single 
diagram which exhibits the equivalent expansion in a single 
cylinder. The area of the figure so drawn is equal to the sum of 
the areas of the high-pressure and low-pressure diagrams. 

In a tandem compound engine of the receiver type the 
diagrams resemble those shown in fig. 61. During CD (which 

Fia. 61. Compound Diagrams : Beoeiver type. 

corresponds to FO) expansion is taking place into the large or low 
pressure cylinder. D and mark the point of cut-off in the 
large cylinder, after which OH shows the independent expansion 
of the steam now shut within the large cylinder, and DE shows 
the compression of steam by continued discharge from the small 
cylinder into the receiver. At the end of the stroke the receiver 
pressure is OE, and this must be the same as the pressure at (7, if 
there is to be no ' drop.' In the diagram sketched it is assumed 
that there is none. The case of ' drop ' would be illustrated if we 
were to cut off the comer at (7 by a vertical line drawn from some 
earlier point in BC to meet the curve CD ; this would of course 


also imply a shortened high-pressure stroke. Diagrams of a simi- 
lar kind may be sketched without difficulty for the case of a re- 
ceiver engine with any assigned phase-relation between the pistons. 
It may be noticed in passing that an intermediate receiver has 
the thermodjmamic advantage that it reduces the range of tem- 
perature in the high-pressure cylinder, and so helps to prevent 
initial condensation of the steam. This will be made obvious by 
a comparison of fig. 60 and fig. 61. The lowest temperature 
reached in the high-pressure cylinder is that corresponding to the 
pressure at D, and is materially higher in fig. 61 than in fig. 60. 

143. AcUustment of the division of work between the 
cylinders^ and of the drop. Graphic method. By making 
the cut-oflf take place earlier in the large cylinder we increase the 
mean pressure in the receiver; the work done in the small 
cylinder is consequently diminished. The work done in the large 
cylinder is correspondingly increased, for the total work (depending 
as it does almost wholly on the initial pressure and the total ratio 
of expansion) is unaflfected or scarcely aflfected by the change. 
Hence we have the apparently anomalous result that a shorter 
admission to the low-pressure cylinder causes it to do a larger 
share of the whole work. 

Further, the same adjustment — namely, hastening the cut-ofi^in 
the low-pressure cylinder — serves, in case there is * drop,' to remove 
it. By selecting suitable values of the ratio of cylinder volumes 
to one another and to the volume of the receiver, and also by 
choosing a proper point for the low-pressure cut-oflf, it is possible 
to secure absence of drop along with equality in the division of 
the work between the two cylinders. 

To determine beforehand that point of cut-oflF in the low- 
pressure cylinder which will prevent drop when the ratio of 
cylinder and receiver volumes is assigned is a problem most easily 
solved, or approximately solved, by a graphic process. The process 
consists in drawing the curve of pressure during admission to the 
low-pressure cylinder until it meets the curve of expansion which 
is common to both cylinders \ In fig. 62 (where for the sake 
of simplicity the eflfects of clearance are neglected) AB represents 
the admission line and BG the expansion line in the small 

1 See a paper by Prof. B. H. Smith, '* On the Cut-off in the Large Cylinder of 
Compound Engines," The Engineer, November 27, 18S5. 



cylinder. Release occurs at C, and from (7 to D steam is being 
taken by the large cylinder. D corresponds to the cut-off in the 



Fza. 62. 

Fia. 63. 

Fios. 62 and 63. — ^Determination of the point of ont-off in the low-piessore 
cylinder of a oomponnd engine. 

large cylinder, which is the point to be found. Prom D to E 
steam is being compressed into the receiver. To avoid drop the 
receiver pressure at £^ is to be the same as the pressure at C. E 
is therefore known, and may be employed as the starting-point in 
drawing a curve EF which is the admission line of the low-pres- 
sure diagram EFOHL This line is drawn by considering at each 
point in the low-pressure piston's stroke what is then the whole 
volume of the steam. The place at which EF intersects the 
continuous expansion curve BCQ determines the proper point of 
cut-off. The sketch (fig. 62) refers to the case of a tandem 
receiver engine ; but the process may also be applied to an engine 
with any assumed phase-relation between the cranks. Fig. 63 
shows a pair of theoretical indicator diagrams determined in the 
same way for an engine with cranks at right angles, the high- 
pressure crank leading. In these examples the volume of the 
receiver has been taken equal to the volume of the high-pressui*e 
cylinder. With a larger receiver the variations of pressure during 
the back stroke of the high-pressure piston would be less con- 
spicuous. In using the graphic method any form may be assigned 
to the curve of expansion. Generally this curve may be treated 
without serious inaccuracy as a common hjrperbola, in which the 
pressure varies inversely as the volume. The construction may 
obviously be applied to triple and quadruple expansion engines. 
For an accurate solution it would be necessary to take the effect 


of clearance into account and also to allow for some loss of pressure 
in the passage from one vessel to another. The figures given here 
omit these complications, and treat the expansion as hyperbolic. 

144. Algebraic Method. When this simple relation be- 
tween pressure and volume is assumed, it is not difficult to find 
algebraically the low-pressure cut-oflf which will give no drop, with 
assigned ratios of cylinder and receiver volumes. Taking the 
simplest case — that of a tandem engine, or of an engine with 
parallel cylinders whose pistons move together or in opposition — 
we may proceed thus. Since the point of cut-off to be determined 
depends on volume ratios we may for brevity treat the volume of 
the small cylinder as unity. Let R be the volume-ratio of the 
receiver to the small cylinder, and L the volume-ratio of the large 
to the small cylinder. Let x be the required fraction of the stroke 
at which cut-oflf is to occur in the large cylinder ; and let p be the 
pressure at release from the small cylinder. As there is to be no 
drop,jp is also the pressure in the receiver at the beginning of 
admission to the large cylinder. During ^ that admission the 
volume changes from l + iZ to 1— a; + J? + xL, and the pressure 

at cut-oflf is therefore ^ ^^ — n . r • The steam that remains is 
1 — a? + jK + wJj 

now compressed into the receiver, from volume 1 — a? + ^ to 

Volume R, Its pressure therefore rises to 

p(l + iZ) (1-x+R) 
l-a!-\'R'\'xL' R 
and this, by assumption, is to be equal to p. We therefore have 
(l+i2)(l-a?+-K) = i2(l-a? + E + a;i), 

whence x = -^y — ^ . 

ML + 1 

Thus, with iJ = l and Z = 3, cut-off should occur in the large 

cylinder at half- stroke (which is the case illustrated by the 

diagram of fig. 61); with a greater cylinder ratio the cut-oflf 

in the large cylinder should be earlier, as it is, for instance, in 

fig. 62. 

A similar calculation^ for a compound engine whose cranks are 

at right angles, and in which cut-oflf occurs in the large cylinder 

^ Examples of oalcalations dealing with partioolar arrangements of two and 
three cylinder compound engines will be fonnd in an Appendix to Mr B. Sennett's 
TreatUe on the Marine Steam-Engine, 


before half-stroke, shows that the condition of no drop is secured 

2R(a!L - 1) = 1 - 2Va?(l-a?). 

In some compound engines a pair of high*pressure cylinders 
discharge into a common receiver ; in some a pair of low-pressure 
cylinders are fed from a receiver which takes steam from one 
high-pressure cylinder, or in some instances from two. With 
these arrangements the pressure in the receiver may be kept 
much more nearly constant than is possible with the ordinary 
two-cylinder type. Occasionally compound engines work without 
any mechanical connexion between the cranks, and the pressure 
within the receiver then depends not only on the adjustment of 
the points of cut-oflF but also on the relative frequency of stroke of 
the pistons. 

146. Ratio of Cylinder Volumes. The size of the low- 
pressure cylinder in a compound engine is fixed by reference to 
the power the engine is intended to develope, the speed, the 
given boiler pressure, and the total ratio of expansion. But the 
size of the high-pressure cylinder remains a matter of choice when 
all these things are settled. Say that the total ratio of expansion 
is to be r ; we may choose any ratio L less than r for the volume- 
ratio of the large to the small cylinder. It will then be necessary 
to make the cut-off in the small cylinder happen at a fraction of 

the stroke equal to — in order that the final volume of the steam, 

when it fills the whole of the large cylinder, may be r times its 
initial volume up to the point of cut-off in the small cylinder. 
Thus an earlier or later adjustment of the cut-off in the high- 
pressure cylinder will allow the whole ratio of expansion to take 
whatever value may be wanted, no matter what be the ratio of 
the cylinder volumes. 

Again, as we have seen above, by varying the cut-off in the 
large cylinder we can adjust matters so that equal amounts of 
work are done in both cylinders, irrespective of their sizes. 

But it is only when a suitable ratio of volumes has been 
selected that this adjustment to equalise the work will also secure 
a reasonable absence of 'drop' — or that an adjustment of the 
low-pressure cut-off to avoid drop will not too seriously disturb 
the balance of work. 


This consideration serves to fix in a general way the proper 
proportion of the volumes. No hard and fast rule is followed ; an 
exact balance in the work is not essential, and a complete absence 
of drop is not even desirable. The same practical considerations 
which make it undesirable in a simple engine to have complete 
expansion (§ 97) apply in regard to compound engines : unless 
there is some little drop the last part of the stroke is ineflfective. 
It should also be remembered that drop in a compound engine is 
not quite so wasteful as it looks : the unresisted expansion into 
the receiver serves to dry the steam and in extreme cases even to 
superheat it. 

Another consideration enters into the question. In some 
engines, especially marine engines, it is a point of importance to 
avoid having an early cut-oflf in any of the cylinders, partly to 
avoid unnecessarily severe stresses in the mechanism and partly 
to allow the valves to be of the simplest kind. This may 
lead to the existence of more drop than would otherwise be 
permissible. In practice the choice of volume ratios is to some 
extent a compromise between conditions that are more or less 
incompatible, and, as might be expected, a good deal of variety 
is found. 

In a two-cylinder compound condensing engine, for instance^ 
using steam of 80 or 90 lbs. pressure the large cylinder may have 
from three to four times the volume of the small cylinder. The 
steam in this case should expand about 12 times ; if a ratio of 3 to 
1 be chosen the conditions of equal work and very little drop will 
be secured by putting the cut-oflF at something like one-fourth of 
the stroke in the high-pressure cylinder and at about one-sixth of 
the stroke in the low-pressure cylinder. An example will be found 
in the indicator diagrams given below in fig. 65. On the other hand, 
if the high-pressure cylinder have only one-fourth of the volume of 
the other, a later cut-oflF will serve. The suitable ratio of volumes 
depends on the boiler pressure; thus if it is 3^ with 70 lbs. it may 
be as much as 4^ with 100 lbs. 

In triple-expansion engines, where the boiler pressure is rarely 
less than 150 nor more than 180 lbs., the third cylinder has 
usually, in marine practice, from 6 to 7 times the capacity of the 
first cylinder, and the second cylinder has from 2J to 2f times 
that of the first. In land engines of this type, where an earlier 
cut-off may be resorted to without inconvenience, the first cylinder 


may be rather larger : its capacity ranges from about one-fifth to 
one-sixth that of the low-pressure cylinder. 

146. Advantage of Oompound Ezpantion in the eco- 
nomical 11M of High-PreMure Steam. The thermodynamic 
advantage of compound expansion has been pointed out in 
§ 114. It allows high-pressure steam to be used without the 
excessive waste which would occur if a high grade of ex- 
pansion were attempted in a single cylinder. So long as the 
boiler pressure does not exceed 100 lbs. this advantage is suf- 
ficiently secured by dividing the expansion into two stages: 
accordingly the ordinary compound engine or two-stage expansion 
engine is used with pressures up to 100 lbs. but not with higher 
pressures. Beyond this triple expansion becomes necessary if the 
full benefit of the higher pressure is to be secured. But when 
the expansion is divided into three stages it becomes advan- 
tageous to use a pressure considerably higher than the limit we 
have just named : thus with triple engines a pressure of 160 to 
170 lbs. is usual. Intermediate pressures, of say 120 or 130 lbs., 
are rarely found: they are too high to suit the two-cylinder 
compound engine and too low to let triple expansion give its 
best effects. Quadruple expansion only becomes desirable when 
the pressure exceeds say 190 lbs. ; up to this pressure the thermo- 
dynamic benefit of a fourth stage is scarcely suflScient to justify 
the mechanical complication it involves. With the types of 
boilers that are ordinarily used this limit of pressure cannot well 
be much exceeded and consequently the quadruple engine is not 

147. Mechanical advantage of Oompound Expansion. 
Unilbrmity of Effort in a Compound Engine. A simple 
engine using high-pressure steam with an early cut-off has the 
drawback, from the mechanical point of view, that the thrust of 
the steam on the piston during the early part of the stroke is very 
great in comparison with the mean thrust. The initial pressure of 
the steam acts on the full area of a piston whose size is determined 
by reference to the mean pressure. The piston and connecting 
rod, the framing and other parts of the machine must be made 
strong enough for this relatively great initial thrust, also there is 
much wear and tear at joints, and for steady motion a large fly- 
wheel becomes necessary. 


The compound engine avoids the extreme thrust and pull 
which would have to be borne by the piston-rod of a single-cylinder 
engine working at the same power with the same initial pressure 
and the same ratio of expansion. If all the expansion took place 
in the low-pressure cylinder, the piston at the beginning of the 
stroke would be exposed to a thrust greater even than the sum of 
the thrusts on the two pistons of a compound engine of equal 
power. Thus in the tandem engine of fig. 60 the greatest sum of 
the thrusts will be found to amount to less than two-thirds of the 
thrust which the large piston would be subjected to if the engine 
were simple. The mean thrust throughout the stroke is of course 
not aflfected by compounding ; only the range of variation in the 
thrust is reduced. The eflFort on the crank-pin is consequently 
made more uniform, the strength of the parts may be reduced, and 
the friction and wear at joints is lessened. Thus even in a tandem 
compound engine there is mechanically some advantage, and the 
benefit of compounding in this respect is obviously much greater 
when the cylinders are placed side by side, instead of tandem, and 
work on cranks at right anglea As a**set-off to its advantage in 
giving a more uniform eflFort, the compound engine has the draw- 
back of requiring more working parts than a simple engine with one 
cylinder. But in many instances — as in marine engines — two 
cranks and two cylinders are in any case almost indispensable, to 
give a tolerably uniform eflfort and to get over the dead-points 
without the aid of a heavy fly-wheel ; and the comparison should 
then be made between a pair of simple cylinders and a pair of com- 
pounded cylinders. Another point in favour of the compound 
engine is that, although the whole ratio of expansion is great, there 
need not be a very early cut-oflf in either cylinder ; hence the com- 
mon slide-valve, which is unsuited to give an early cut-oflF, may be 
used in place of a more complex arrangement. The mechanical 
advantage of compound working was recognized sooner than its 
thermodynamic economy, and did much to bring it into favour 
before, indeed, the practice had grown up of using steam high 
enough in pressure to make compounding very distinctly econo- 

Again, apart from its improved economy the mechanical merits 
of the triple engine have contributed much to bring it quickly to 
the position it now holds in marine practice. The advantage of 
three cranks over two in giving uniform effort and comparatively 



little friction and wear is conspicuous, and a triple engine with its 
three cranks set at 120° from each other is now the standard 
marine type. 

148. Examples of Indicator Diagrams flrom Oompound 
Engines. Fig. 64 shows a pair of diagrams from the two cylin- 

Fio. 64. Indicator Diagrams of a Woolf Engine. 

ders of a Woolf engine, in which the steam passes as directly as 
possible from the small to the large cylinder. Both pistons have 
the same length of stroke. The diagrams are drawn to the same 
scale of stroke and therefore to different scales of volume, and the 
low-pressure diagram is turned round so that it may fit into the 
space below the high-pressure diagram. There is some drop at 
the high-pressure release, and further the Motion of the passages 
causes the admission line of the large cylinder to lie slightly lower 
than the exhaust line of the small cylinder. The transfer of steam 
goes on throughout nearly the whole of the back stroke until 
compression begins in the small cylinder. The steam then present 
in the large cylinder continues expanding for the small part of the 
stroke that is left until the point of release is reached. 

An example of compound diagrams for an engine of the receiver 
type has already been given in figs. 60 and 51, Chap. VI. 

The receiver in that engine was unusually large, which ac- 
counts for the nearly level line drawn during the back stroke of 
the small piston. Another example is given in fig. 66 which 
shows the diagrams of a tandem receiver engine with cylinders 30 
and 62 inches in diameter and 6 ft. stroke (volume ratio 1 to 3), 
taking steam at an initial pressure of 80 lbs. above the atmosphere. 
With this proportion of volumes and with the somewhat early 
cut-off shown by the diagrams there is a complete absence of any 



objectionable drop and a nearly equal division of work between 
the cylinders. Expansion valves (see Chap. VIII.) were used to 

Atmospheric Line 

Fio. 66. 

produce this early cut-oflf. The exhaust line of the small cylinder 
dips in the middle, as in fig. 62, but much less, for here the receiver 
is more capacious. When the cranks are set at right angles this 
line rises towards the middle as fig. 63 indicates. 

Fig. 66 shows a set of triple expansion diagrams, from trials 
(by a Committee of the Institution of Mechanical Engineers) of 
the steamship " lona." The cylinder diameters were 21*9 in., 
34 in. and 57 in., giving a volume ratio of 1 : 3 : 6f , and the stroke 
was 39 in. The engines made 61 revolutions per minute and 
developed 208 LH.P. in the first cylinder, 217 in the second and 
220 in the third, with a consumption of 13*35 lbs, of steam per 
I.H.P.-hour. A simple slide-valve was used on each cylinder ^ 

149. Oomblnatlon of the Indicator Diagrams in Oom- 
pound Expansion. The indicator diagrams of a compound engine 
may be combined in such a way that the pressures and volumes 
in the several cylinders are displayed in proper relation to one 
another, by the use of a single scale of pressures and a single scale 
of volumes. Some care, however, is necessary in the interpretation 
of such combined diagrams, and the construction to be adopted 
will depend on the use that is aimed at. 

^ Report of the Besearoh Gommiitee on ICarine Engine Trialfl, Proc, In$U Mech. 
£n^., April, 1891. 

E. 14 



A common practice is to set out each diagram from the line of 
no volume through a distance which represents the clearance in 
the corresponding cylinder. This is illustrated in fig. 67 which 
has been drawn to exhibit in combination the diagrams already 
shown in figs. 50 and 51, § 126. Each of the two diagrams 
in fig. 67 is a mean for the two sides of the piston and the 

Fio. 66. 

distance of each from the line OF is the mean clearance in 
the corresponding cylinder. Diagrams drawn in this way are 
not without their uses, but it must be remembered that the 
amount of substance which is taking part in the expansion is 
different in the two parts of the combination, and consequently a 



single adiabatic curve or a single saturation curve cannot properly 
be drawn to apply to both. The line 88 is the saturation curve 
for the first stage of expansion, and the line 8^8^ for the second 
stage. In this example the cylinder feed per single stroke was 
0*0498 lbs., and the cushion steam was 0*0074 lbs. in the small 
cylinder and 0*0022 lbs. in the large cylinder. The saturation 

fia. 67. 

curve 88 is accordingly drawn for 00672 lbs. and 8'8' for 0*052 lbs. 
The amount of the substance is in general different in the successive 
stages because of differences in the amount of cushion steam in 
the several cylinders: the cylinder feed is the same throughout. 
If therefore we modify the diagram in such a way as to eliminate the 
cushion steam, leaving the cylinder feed only, we may draw a single 
saturation curve which will serve for all the expansion. 

This is done in fig. 68, which represents the same pair of dia- 
grams, transformed by the following device. From points D, ly 
(fig. 67) taken at the places where compression has begun and the 
exhaust is complete, saturation curves are drawn for the cushion 
steam in the respective cylinders. These curves are indicated by 
broken lines in the figure : the one that relates to the small cylinder 
is scarcely distinguishable from the compression curve of the indica^ 
tor diagram. The diagrams are tbeu redrawn as in fig. 68, using 




horizontal distances from these curves as abscissae. This is equiva- 
lent to subtracting from the actual volumes throughout the diagram 
a quantity which represents the volume the cushion steam would 
occupy if it were saturated at all pressures. The result is that 
the area of the diagram remains unaltered : its area is still a true 
measure of the work. But a single saturation curve S^S^ may now 
be drawn — namely for a quantity of steam equal to the cylinder 
feed — which will apply equally to both (or all) stages of the com- 
pound expansion. The horizontal distance at any pressure between 
the expansion curve in fig. 68 and the saturation curve S^S^ is 


Fia. 68. 

the same as the horizontal distance at that pressure between 
the expansion curve in fig. 67 and its corresponding saturation 
curve. It still represents the volume which has disappeared by 
condensation or what is often called the ' missing quantity.' The 
chief advantage of this construction is that it makes a single 
saturation curve possible, and so allows the changes in the amount 
of water present to be readily exhibited as the steam passes 
through the whole course of its expansion. 

This will be apparent from figs. 69 and 70 which are copied 
from Professor Osborne Reynolds' account of triple engine trials^ 

I Min. Proc. Intt C. E., VoL xo. 


to which reference was made in Chapter V. Here the cushion 
steam has been eliminated in the manner just described and a 
single saturation curve has been drawn for the cylinder feed. The 
horizontal width of shaded space between the actual expansion 

Cub. Ft per lb. 
Fia. 69. 

curves and this line measures the water present at any stage in 
the expansion. Fig. 69 refers to a test made without steam in 
the steam-jackets, and fig. 70 to a test when all the jackets were 
supplied with steam at the full boiler pressure of 190 lbs. The 

drying influence of the jacket is conspicuous : in fig. 70 there is 
scarcely any condensation in the third cylinder. 


These diagrams relate to an engine built for experimental use 
in which the three pistons could move independently, at different 
speeds, and the speeds were in fact different. Hence to prepare 
the diagrams for combination a further device was employed : the 
common scale of length of the diagrams was chosen so that the 
volumes represented in each are reckoned per lb. of cylinder feed. 
The scale of volume is accordingly divided in the figures to show 
cubic feet per lb. of water passing through the engine. This is a 
method of graduation which might be followed with advantage 
even in ordinary cases, where it is not rendered necessary by the 
pistons having independent speeds, for it facilitates comparison 
between various trials. 



160. The Slide- Valve. In early steam-engines th^ dis- 
tribution of steam was eflfected by means of conical lift-valves, 
rising and falling on conical seats, and worked by tappets from a 
rod which hung from the beam. The slide-valve, the invention of 
which is credited to Murdoch, an assistant of Watt, came into 
general use with the introduction of locomotives, and is now 
employed, in one or other of many forms, in the great majority of 

The common or locomotive slide-valve is illustrated in fig. 71 
which shows a sectional side and end elevation and a plan« The 
jseat, or surfeu^e on which the valve slides, is a plane surface formed 

Fzo, 71. Ck>inmoii Slide-Valve. 


on or fixed to one side of the cylinder, with three ports or 
openings, which extend across the greater part of the cylinder's 
width. The ports are shown in the plan by dotted lines. The 
central opening is the exhaust-port through which the steam 
escapes ; the others, or steam-ports, which are narrower, lead to 
the two ends of the cylinder respectively. The valve is a box- 
shaped cover which slides upon the seat, and the whole is enclosed 
in a chamber called the valve-chest, to which steam from the 
boiler is admitted. The valve is pulled backwards and forwards 
across the ports by m0&ns of a valve-rod which passes out of 
the valve-chest through a steam-tight stuffing-box. The valve is 
attached to the valve-rod not rigidly but in such a way that, 
while it has no longitudinal freedom to slide along the rod, it is 
free to take a close bearing on the seat, under the pressure 
exerted by the steam on its back. In its middle position the 
valve covers both steam-ports completely, but when it is moved a 
sufficient distance to either side of the middle position, it allows 
fr^sh steam to enter one end of the cylinder fit)m the valve- 
chest, and allows the steam which has done its work to escape 
fit)m the other end of the cylinder through the cavity of the 
valve into the exhaust-port. The valve-rod is generally moved by 
an eccentric on the engine-shaft, which is mechanically equivalent 
to a crank whose radius is equal to the eccentricity, or distance of 
the centre of the shaft fi^m the centre of the eccentric disc or 
sheave. The sheave is encircled by a strap to which the 
eccentric-rod is fixed and the rod is connected by a pin-joint 
to the valve-rod outside of the valve-chest. The eccentric-rod is 
generally so long that the motion of the valve is sensibly the same 
as that which it would receive were the rod 
infinitely long. Thus if a circle (fig. 72) be 
drawn to represent the path of the eccentric- 
centre during a revolution of the engine, and 
a perpendicular PM be drawn from any point P 
on a diameter AB, the distance CM is the 
displacement of the valve from its middle posi- '^' ' 

tion at the time when the eccentric-centre is at P. AB is the 
whole travel of the valve. 

161. laap^ Lead^ and Angular Advance. If the valve 
were formed so that. when in its middle position it did not overlap 



the steam-ports (fig. 73), any movement to the right or the left 
would admit steam, and the admission would continue until the 
valve had returned to its middle position, or, in other words, for 

Fio. 78. Slide-Valve without Lap. 

half a revolution of the engine. Such a valve would not serve for 
expansive working; it would admit steam to one end of the 
cylinder during the full stroke, and at the same time would exhaust 
steam from the other end during the full stroke. As regards the 
relative position of the crank and eccentric it would have to be set 
so that its middle position was coincident in point of time with the 
extreme position of the piston; in other words the eccentric 
radius would have to make a right angle with the crank. 

To make expansive working possible the valve must be able to 
keep the cylinder ports closed during some part of the stroke. 
For this purpose it must have what is called Zap, that is to say its 
edges must project beyond the ports as in fig. 74, where e is the 
outside lap and i is the inside lap. Admission of steam to either 

Fio. 74. 

Slide- Valve with Lap. 

end of the cylinder now begins only when the displacement of the 
valve from its middle position is equal to the outside lap, and 
continues only until the valve returns to the same distance fix)m 
its middle position. Further, exhaust begins only when the valve 
has moved past the middle position by a distance equal to the 
inside lap and continues until the valve has again returned to 



this distance fi*om its middle position. Thus let a circle (fig. 75) 
be drawn to represent the path of the eccentric-centre, on a 

Fio. 76. 

diameter fg which is the whole travel of the valve, let om be set 
off equal to the outside lap e and (m to the inside lap t, and let 
perpendiculars aimb and ond be drawn at these distances from the 
centre. The points a, 6, o and d then mark the positions of the 
eccentric-centre at which the four events of admission, cut-off> 
release and compression respectively occur for one end of the 
cylinder. As to the other end the four events are determined in 
the same way by setting off the corresponding outside lap to the 
lefb of and the inside lap to the right of o. The laps may or 
may not be equal for the two ends of the cylinder. For the sake 
of clearness we may for the present confiiie our attention to one of 
the two. Of the whole revolution the part from a to 6 is the arc 
of admission ; in other words, the port is open to steam while the 
shaft turns through an angle equal to (wh. Similarly ho is the arc 
of expansion, cd that of exhaust and da that of compression. 

The relation of these events to the piston's position is still 
undefined. If the eccentric were set in advance of the crank by 



an' angle equal to foa, the valve would be just beginning to open 
as the piston stroke begins. It is, however, desirable, in order to 
allow the steam free entry, that the valve should be already some 
way open when the piston stroke begins, and hence the eccentric 
is set at a rather greater angular distance in advance of the crank. 
Thus if the angular position of the eccentric is ob while the crak^k 
is at the dead-point (op the line of) the vfi^lve is c^lready open by 
the distance mg. which is called the had. The angle ^ by which 
the whole angle between the crank and the eccentric exceeds a 
right angle is called the angular advance, this being the angle by 
which the eccentric is set in advance of the position it would hold 
if the primitive arrangement without lap were adopted. The 
quantities lap 6, lead I, angular advance 0, and half-travel or 
throw of the eccentric r are Qonnected by the equation 

e + i == r sin ^. 

An effect of lead is to cause preadmission, that is to say the lead 
allows steam to enter before the back stroke is quite completed, 
and this increases the mechanical effect of the compression in 
" cushioning " the piston during the reversal of its motion. ^ 

The greatest amount by which the valve is ever open during" 
the admission of steam is the distance mg. The width of the 
steam port is made at least equal to this distance, and is often 
greater in order that the wider opening nf which occurs during 
exhaust may be taken advantage of. 

162. Graphic method of ezamlning the distribution of 
steam given by a slide-valve. Let the circle APB (fig. 76) 
represent the path of the crank-pin about the centre 0, the stroke 


being AB, When the crank is at any point P the position of the 
piston may be found by projecting the point P on AB by draMring 



a circular arc PD with the length of the eonnecting-rod PQ as 
radius and the cross-head Q as centre. Then DO represents the 
displacement of the piston from its middle position, and AD and 
DB represent its distance from the two ends of the stroke. Another 
construction equivalent to this is to draw through the arc OM 
with the length of the connecting-rod as radius, and draw PM 
parallel to AB. PM, being equal to DO, measures the displace- 
ment of the piston from its position at mid-stroke. In speaking of 
the two ends of the cylinder we shall distinguish the one nearer 
the crank as the front end and the other as the back end. The 
stroke towards the crank may be called the in-stroke and the 
other the out-stroke, as marked in fig. 76. 

To find the position of the piston at each of the four events we 
have to make a construction which is equivalent to transferring 

Fio. 77. 



from fig. 75 the four positions of the crank which correspond to 
the positions a, b, c, d of the eccentric. This is most readily done 
by (tawing a single circle (fig. 77) to represent the motion of the 
crank-pin on one scale and the motion of the eccentric-centre on 
another scale. Taking the diameter AB to represent the piston 
stroke, draw another diameter hk to represent the line hk of 
fig. 75 turned back through an angle of QO'' + ^, so that the angle 
AOh (fig. 77) is equal to 0, Draw ab and cd parallel to this line 
at distances from it equal to the outside and inside laps respect- 
tively. The effect is that each of the points a, b, c and d is turned 
back, in fig. 77, through an angle equal to 90'' + ^ as compared 
with its position in fig. 75. Consequently these points in fig. 77 
show the positions which the crank has at the four events. And 
the corresponding positions of the piston may be found by 
projecting the points a, 6, c, d on AB by means of circular arcs. 
This is shown in fig. 77, and the indicator diagram is also 
sketched by reference to the positions projected on AB, 

The following is an equivalent and rather more convenient 
construction. Let the circle (fig. 78) be drawn as before to 

Fio. 78. 

represent the eccentric's motion on one scale and the crank's on 
another, and let AB be the piston stroke. Draw hk as before so 
that the angle AOh^B, the angular advance. Taking a centre 


on OA produced, draw the arc EOF through the centre with 
radius equal to the length of the connecting-rod. Then when 
the crank has any position OP the displacement of the valve 
from its middle position is PN (drawn perpendicular to hk) and 
the displacement of the piston from mid-stroke is PM. Also, if 
db and cd be drawn as before at distances from hk equal to the 
laps, the four events happen at a, b, c, and d, and PQ is the extent 
to which the valve is open when the crank is at P. Similarly 
AL is the extent to which the valve is open at the beginning of 
the stroke, that is the lead. The port has its maximum opening 
when the crank is at Og during admission and at Of during 
exhaust unless its width is so small that it has become com- 
pletely uncovered with a smaller displacement of the valve. 

The diagram shown in fig. 78, which is a modified form of one 
due to Reuleaux, may readily be applied to determine the charac- 
teristics which a slide-valve must have to give a stated distribution 
of steam. Suppose for instance that the travel of the valve, the 
lead, and the position of cut-off are assigned. Having marked b, 
the position of the crank-pin at the given point of cut-off in rela- 
tion to the stroke AB, draw a circle with centre A and radius AL 
equal to the lead. Then di:aw a line through b tangent to this 
circle. This will be the line ba of the diagram. Its inclination 
to BA determines the angular advance and a perpendicular on it 
from gives Om which is the outside lap. The inside lap becomes 
determinate when either the point of release c or that of compres- 
sion d is assigned, and it is found by drawing a line through c or 
d parallel to ab, and measuring the distance of this line from 0. 

163. Inequality of the distribution on the two sides of 
the piston. So far we have dealt only with the events corre- 
sponding to one end of the cylinder, namely (in the diagram) the 
back end. This has been done only to avoid complicating the 
diagram with too many lines. In fig. 79 the construction of 
fig. 78 is repeated with the outside lap lines ab and a'6' drawn for 
both ends, and also the inside lap lines cd and cd', and the 
correspoudiug events are marked. The construction lines relating 
to the front end of the cylinder are distinguished by being dotted 
and their reference letters are accented. The laps have been 
taken equal for the two ends, and an obvious result is that 
the cut-off is considerably later at the back than at the front. 



Compare bm with 6W, these being the distances by which 
the piston has passed mid-stroke when the cut-off occurs at 


Fio. 79. 

the back and front respectively. This want of symmetry, pro- 
ceeding as it does from the obliquity of the connecting-rod, is 
slight when the rod is many times longer than the crank but becomes 
important when the rod is short. In the sketches, the length of 
the rod is supposed to be three times that of the crank. 

This inequality may be remedied by making the outside laps 
unequal, giving less lap to the front end of the valve. When this 
is done, however, the amounts of lead (which are equal with equal 
laps) become unequal. But in general it is better to sacrifice equal- 
ity of lead and to secure at least approximate symmetry in the 
positions of the two points cut-off, when the admission of steam is 
controlled by a simple slide-valve. When a separate expansion 
valve is used (§ 161 below) the cut-off is determined by it, and not 
by the main slide-valve, and in that case the amounts of lead may 
properly be made equal. In some cases a somewhat unequal 
distribution of steam is to be preferred, as in the ordinary vertical 
marine engine, where the work done by the steam sigainst the 
front or bottom end of the piston is partly spent in raising the 
piston and rods and consequently should be greater than the 



work done against the back or top end which is supplemented 
by the descent of these heavy weights. This difference may be 
allowed for by providing a later cut-off at the £ront than at the 
back, which is done by making the laps still more unequal than 
a symmetrical distribution would require. 

In cases where the eccentric-rod is itself so short that its 
obliquity should be taken account of, this is readily done in 
Reuleaux's diagram (fig. 78 or 79) by using circular arcs in place 
of the straight lines oi, hk^ cd, these arcs being described with a 
radius which represents the length of the eccentiic-rod on the 
same scale as that on which the diameter AB represents the travel 
of the valve, from centres on Of produced beyond /• Except in 
rare cases it leads to no appreciable error to treat the eccentric-rod 
as infinitely long. 

Fig. 80 illustrates how a symmetrical distribution is secured 
by reducing the outside lap at the front end. There oft is 

Fio. 80. 

the outside-lap line for the back end and a'b' is the corresponding 
line for the front end. These lines are drawn so that the cut-off 
occurs at the same percentage of the stroke at both ends: bm 
and Vm' are equal. The inside laps may also be adjusted in the 
same way to give equal amounts of compression on both strokes 
(or, alternatively, to give symmetrical points of release). The 
amounts of lead, of course, are no longer equal : the lead at the 


front end has been considerably increased by the reduction of the 

164. Zeuneir'B Valve Diagram. The graphic construction 
most Tisually employed in slide-valve investigations is the in- 
genious diagram published by Dr G. Zeuner in the Civilingenieur 
in 1856\ On the line AB (fig. 81), which represents the travel 
of the valve, let a pair of circles (called valve-circles) be drawn, 

Fio, 81. 

each with diameter equal to the half-travel. If a radius CP be 
drawn in the direction of the eccentric centre at any instant, it is 
cut by one of the circles at a point Q such that CQ represents the 
corresponding displacement of the valve from its middle position. 
That this is so will be seen by drawing PM and joining QB, when 
it is obvious that the triangles CPM and CBQ are equal in all 
respects and CQ — CM, which is the displacement of the valve. 
The line AB with the circles on it may now be turned back 
through an angle of 90"" + 0.(0 being the angular advance), so that 
the valve-circles take the position shown to a larger scale in 
fig. 82. This makes the direction of CQP (the eccentric) coincide 
on the paper with the simultaneous direction of the crank, and 
hence to find the displacement of the valve at any position of the 
crank we have only to draw the line CQP in fig. 82 parallel to the 
direction which the crank has at the instant under consideration, 
when CQ represents the displacement of the valve to the 
scale on which the diameter of each valve-circle represents the 

' Zetmer, Treatise on Valve-Oeart, transl. by M. MuUer, 1868. 
E. 15 



half-travel of the valve. CL is the valve's displacement at the 
beginning of the stroke indicated by the arrow. Draw circular arcs 

Fia. 82. Zeaner*8 Slide-Valve Diagram. 

EF and IJ with G as centre and with radii equal to the outside 
lap and the inside lap respectively. GE is the position of the 
crank at which preadmission occurs. The lead is LM, The 
greatest steam opening during admission is OB and the greatest 
opening to exhaust is the whole width of the port, namely KH. 
Intercepts on the radii within the shaded areas give the steam 
and exhaust openings for any angular positions of the crank. 
The cut-off occurs when the crank has the direction GF, GI is 
the position of the crank at release, and GJ marks the end of 
the exhaust, or the beginning of compression. 


In the diagram given in fig. 82 radii drawn from G mark the 
angular positions of the crank, and their intercepts by the valve- 

Fio. 83. Zenner's constrnotion to find the displacement of the piston. 

circles determine the corresponding displacement of the valve. It 
remains to find the corresponding displacement of the piston. For 
this Zeuner employs a supplementary graphic construction, shown 
in fig. 83. Here ah or Oi^i represents the connecting rod, and he 
or 6iC the crank. With centre c and radius dc a circle op is 
drawn, and with centre h and radius ah another circle aq. Then 
for any position of the crank, as c6i, the intercept pq between the 
circles is equal to ooi, and is therefore the distance by which the 
piston has moved from the extreme position which it had at the 
beginning of the stroke. In practice this diagram is combined with 
that of fig. 82, by drawing both about the same centre and using 
different scales for valve and piston travel. A radial line drawn from 
the centre parallel to the crank in any position then shows the 
valve's displacement from its middle position by the intercept QQ 
of fig. 82, and the simultaneous displacement of the piston from the 
beginning of its motion by the intercept pq of fig. 83. As an 
alternative to this the piston's displacement may be found in 
Zeuner s diagram by the construction used in Reuleaux's, which 
was described in connection with figs. 77 and 78. 



As an example of the application of Zeuner's diagram we may 
take the same problem as before, namely to find the outside lap 
and angular advance when the point of cut-off and the lead for the 
corresponding side of the piston are assigned, as well as the travel 
of the valve. The solution is shown in fig. 84. On the base-line 

Fio, 84. 

XX' mark the point M to represent the required point of cut-off 
and project this on the circle XPX' to find CP which is the 
angular position of the crank at cut-off. With X as centre draw 
a circle with radius XN to represent the given lead. From P 
draw PN tangent to this circle. Then COB drawn perpendicular 
to PiV^ defines the diameter of the valve-circle. The angle X'GB is 
the angular advance, plus 90°, and CO is the required outside lap. 
So far as the simpler problems of the slide-valve are concerned 
Zeuner's diagram has no marked advantage over Reuleaux's. It is 
however more readily applicable to cases where the events of the 
stroke depend on the movements of more than one eccentric, as, 
for instance, in the Meyer expansion gear to be presently described. 

166, Oral Diagram. A diagram is sometimes drawn which 
represents by a single curve the simultaneous displacements of the 
piston and the valve. When the position of the valve has been 
determined at various phases of the piston's stroke, whether by 



Reuleaux's or Zeuner's or any other method, a curve is drawn 
having for ordinates the displacement of the valve, on a base AB 
(fig. 85) which is the stroke of the piston, the scale of the ordinates 
being suitably exaggerated to prevent the curve from being 

Fio. 85. Oval Diagram for the Slide- Valve. 

inconveniently flat on account of the comparatively small ampli- 
tude of the valve's motion. This gives a species of oval figure 
resembling an ellipse but somewhat distorted through the in- 
fluence of the connecting-rod's obliquity. To find the events of 
the distribution, lines EE and // are drawn above and below the 
base at distances from it equal to the outside and inside laps re- 
spectively; their points of intersection with the curve at a, b, c and d 
mark the four events for the corresponding end of the cylinder. For 
the other end the outside lap line E'E' is to be drawn below the 
base and the inside lap line IT above it. The distance of the 
curve beyond the outside lap line shows at any stage in the stroke 
the extent to which the steam port is then open. The lead, which 
is EL, is not well defined in this form of graphic construction. 

166. Harmonic Diagram. A much more useful diagram 
is obtained by drawing (preferably on section paper) separate 
curves to represent the displacements of piston and valve re- 
spectively, each in relation to the angle turned through by the 
crank-shaft. Taking a base (fig. 86) the length of which repre- 
sents the angle turned through in one revolution, let the curve 
A BCD be drawn to represent by its ordinates the displacement 
of the piston from mid-stroke, for all positions of the crank. 



Similarly let a curve EFIJ be drawn with ordinates which are (on 
any conveniently exaggerated scale) the displacements of the valve. 

Fia. 86. Harmonic Diagram for tbe Slide- Valve. 

Owing to the angle between the crank and the eccentric the 
phase of this curve is 90° + ^ in advance of the other : in other 
words the valve attains its maximum displacement at a point on the 
base-line 90"" + earlier than (or to the left of) the point at which 
the piston attains its maximum displacement towards the same 
side. In drawing fig. 86 an angular advance of 30° has been assumed, 
which makes the total displacement of the valve curve to the left 
correspond to 120°. When questions have to be considered re- 
garding the effect of varying the angular advance, one or other of 
the curves should be drawn on tracing paper in order that it may 
readily be slipped over the other into the position that will corre- 
spond to any desired angle. 

Let any line PQR be drawn perpendicular to the base-line to 
intersect the piston curve in P and the valve curve in R. The 
displacement of the piston is then PQ and that of the valve is (on 
another scale) QR, The position of the piston in its stroke is 
found by projecting P upon the end line of the diagram (to the 
left) where a scale is marked to show percentages of the stroke. 
If EF be drawn parallel to the base and at a distance below it equal 
to the outside lap, SR, which is the excess of the valve's displacement 
beyond the lap Q8, gives the steam opening at the same phase of 
the stroke. Admission begins at E, and the corresponding position 
of the piston is found by projecting E upon the piston curve at A 
and then projecting A upon the scale at the side. The vertical 
distance from KU> A shows the amount of preadmission. At K^ 


the dead-point of the crank, the valve is open to the extent LM; 
in other words LM is the lead. Cut-off occurs at F, and the 
corresponding position of the piston is found by projecting F upon 
the piston curve at B, and then projecting B upon the scale at the 
side. In the same way the positions of the piston at release and 
compression correspond to the points / and J on the valve curve 
when the line IJ is drawn at a distance above the base equal to 
the inside lap. All these events relate to one side of the piston ; 
to obtain the events for the other side the outside lap line has to 
be drawn above the base and the inside lap line below it, and the 
points found on the piston curve are to be projected upon the scale 
which is set out on the right-hand side of the diagram in fig. 86. 
The inequality of lap and lead which is needed to give a symmetrical 
distribution, and other such problems of design, may be studied by 
help of this diagram with great ease and clearness^ Another 
example of its use will be given below in connection with separate 
expansion valves (§ 162). 

The ordinates of these curves may be found either by graphic 
construction or by calculation. As to the valve curve, the length 
of the eccentric rod is generally so great that its influence 
may be neglected, and in that case the formula 

y' = r' cos a' 
may be used, r' being the eccentricity or the half-travel of the 
valve and a' being the angle through which the eccentric has 
turned from the position that corresponds to the maximum dis- 
placement of the valve. 

In the piston curve the influence of the rod is usually con- 

Fio. S7. 

siderable. Let r be the effective length of the crank AP (fig. 87) 
and I that of the connecting rod BP ; when the crank has turned 

^ The writer is indebted to Professor O. Beynolds for drawing his attention to 
the advantages of the oonstmotion iUastrated in fig. 86. As a means of solving 
alide-Talve problems it is in several ways superior to the methods more generally used 
by draoghtsmen. See a paper by Bfr W. E. Dalby, Engineering, April 7, 1898. 


through any angle a from the dead-point the displacement of the 
piston from its middle position is 

= r cos a + VP — r* sin' a — /, 
or, writing fi for the ratio of the length of the connecting rod to 
that of the crank, 

y = r (cos a + \/fi^ — sin* a — fi). 
This is always less than rcosa, but approximates closely to that 
when fi is very great. An expression of the same form is of course 
applicable to the displacement of the valve and should be used 
when the eccentric rod is so short as to require its length to be 
taken into account. The angles a (for the crank) and a' (for 
the valve) are connected by the equation a' = a + 90° + where 
is the angular advance as before. 

167. Reversing Gear. The Iiink-motton. In locomo- 
tives, marine engines, winding engines, traction engines and some 
other types it is necessary to make provision for reversing the 
direction in which the engine runs. A primitive way of doing 
this is to shift the eccentric of the slide-valve round upon the 
shaft until it takes relatively to the crank the angular position 
proper to the reversed motion. The eccentric must stand in 
advance of the crank by an angle equal to 90°-!-^, and if its 
position be CE (fig. 88) while the 
crank is at CK the engine will run 
in the direction of the arrow A. To 
set the engine in gear to run in the 
opposite direction it is only necessary 
to shift the eccentric into the position 
CE', when it will still be in advance 
of the crank by the proper angle, the 
direction of motion now being that Fig. 88. 

shown by the arrow A\ In some of 

the older engines this was substantially the actual method of 
reversal. The valve rod was temporarily disengaged from the 
eccentric and the valve was moved by hand in such a way 
as to make the engine begin to turn backwarda It was 
allowed to turn until the crank had moved back through an 
angle equal to ECE\ the eccentric meanwhile remaining at 
rest, and the valve rod was then re-engaged. To allow the 



eccentric to remain at rest while the crank turned back 
through the required angle, the eccentric sheave instead of 
being keyed to the shaft fitted loosely on it and was driven 
by means of a spur fixed to the shaft which abutted on one or 
other of two stops or shoulders projecting from the sheave. 
Consequently when the engine shaft began to turn backwards the 
eccentric sheave did not at once follow it, until it had turned 
through an angle corresponding to the distance between the two 
stops. This device of the loose eccentric is not entirely obsolete \ 
but nearly all modern engines which require reversing gear use 
either the link-motion or one of the forms of radial gear to be 
presently described. 

In the link-motion there are two eccentrics keyed to the 
shaft in positions which correspond to CE and CE' in fig. 88, and 
the ends of their rods are connected to the ends of a link which 
gives its name to the contrivance. In Stephenson's link-motion — 
the earliest and still the most usual form — the link is a slotted 
bar or pair of bars forming a circular arc with radius equal or 
nearly equal to the length of the eccentric rods (fig. 89), and 
capable of being shifted up and down by means of a pendulum rod 
to which it is jointed either at one end or at the middle of the 
link. This suspension by a pendulum rod also allows the link to 
move sideways as the eccentrics revolve. 

The valve-rod ends in a block which slides within the link, 
and when the link is placed so that this block is nearly in line 
with the forward eccentric rod (iJ, fig. 89) the valve moves in 

Fio. S9. Stephenson's Link-motion. 

^ It is applied for instanoe to the low-pressore valve of Mr Webb's compoand 
locomotives. In this case there is no need to disengage the rod for the engine is 
made to begin turning backwards by the action of the high-pressure cylinders. 



nearly the same way as if it were driven directly by a single 
eccentric. This is the position in "full forward gear." In "full 
backward gear/' on the other hand, the link is pulled up until the 
block is in nearly a line with the backward eccentric rod R. The 
link-motion thus gives a ready means of reversing the engine, — 
but it does more than this. By setting the link in an inter- 
mediate position the valve receives a motion nearly the same as 
that which would be given by an eccentric of shorter throw and of 
greater angular advance, and the effect is to give a distribution of 
steam in which the cut-off is earlier than in full gear, and the 
expansion and compression are greater. Hence the mechanism also 
serves to adjust the amount of work done in the cylinder to the 
demand which may at any time be made upon the engine. In 
mid gear, which is the position sketched in the diagram, the steam 
distribution is such that scarcely any work is done in the cylinder. 
The movement of the link is effected by a hand lever, or by & 
screw, or (in large engines) by an auxiliary steam-engine. A 
usual arrangement of hand lever, sketched in fig. 89, has given 
rise to the phrase " notching up," to describe the setting of the 
link to give a greater degree of expansion, by bringing it nearer 
to mid gear. The eccentric rods are sometimes crossed instead of 
being " open " as shown in the sketch. 

In Gooch*s link-motion (fig. 90) the link is not moved up in 

Fio. 90. Goooh's Link-motion. 

shifting from forward to backward gear, but a radius rod between 
the valve-rod and the link (which is curved to suit the length of this 
radius rod) is raised or lowered — a plan which has the advantage 
that the lead is the same in all gears. In Allan's motion (fig. 91) 
the change of gear is effected partly by shifting the link and 
partly by shifting a radius rod. This allows the link to be 



straight and has also the advantage that the weight of the link 
with its eccentric rod on the one hand, and the radius rod on the 


Fio. 91. Allan's Link-motion, 
other, can be arranged to balance one another when a suitable 
proportion is given to the two arms of the short beam from which 
the pendulum rods hang. 

168. Graphic Solution of the Iiink-motion. The move- 
ment of a valve driven by a link-motion may be fully and 

Fig. 92. 


exactly investigated by drawing with the aid of a template the 
positions of the centre line of the link corresponding to a number 
of successive positions of the crank. Thiis, in fig. 92, two circular 
arcs passing through e and ^ are drawn with E and E as centres 
and the eccentric rods as radii These arcs are loci of two known 
points of the link, and a third locus is the circle a in which the 
point of suspension must lie. By placing on the paper a template 
of the link, with these three points marked on it, the position of 
the link is readily found, and by repeating the process for other 
positions of the eccentrics a diagram of positions (fig. 92) is drawn 
for the assigned state of the gear. A line AB drawn across this 
diagram in the path of the valve's travel determines the displace- 
ments of the valve, and enables the harmonic diagram to be drawn 
as in fig. 86, or alternatively the oval diagram as in fig. 85. The 
example refers to Stephenson's link-motion in nearly full forward 
gear ; with obvious modification the same method may be used in 
the analysis of Gooch's or Allan's motion. The same diagram 
serves to determine the amount of slotting or sliding motion of the 
block in the link. In a well-designed gear this sliding is reduced 
to a minimum for that position of the gear in which the engine runs 
most usually. In marine engines the suspension-rod is generally 
connected to the link at that end of the link which is next the 
forward eccentric, in order to reduce this sliding as much as possible 
when the engine is running in its normal condition, namely, in 
forward gear. 

169. Equivalent eccentric. A less laborious, but less 
accurate, solution of link-motion problems is reached by the use 
of what is called the equivalent eccentric — an imaginary single 
eccentric, which would give the valve nearly the same motion as it 
gets from the link under the joint action of the two actual eccentrics. 
The following rule for finding the equivalent eccentric, in any state 
of gear, is due to Mr MacFarlane Gray : — 

Connect the eccentric centres E and E (fig. 93) by a circular 




, ,. j&^ X lenffth of eccentric rod . , . ,, 
whose radius = — ^ :; , ee being the 

2 xee ' ^ 

length of the link from rod to rod. Then, if the block is at 
any point B, take EF such that EF : EE' :: eB : ee^. CF then 
represents the equivalent eccentric both in radius and in 
angular position. If the rods of the link-motion are crossed 
instead of open, — ^an arrangement seldom used, — the arc EFE' 
is to be drawn convex towards C. Once the equivalent eccentric 
has been found the movement of the valve may of course be 
determined by Zeuner*s or any of the other methods already 
described \ The method of the equivalent eccentric should not be 
taken as giving more than a first approximation to the actual 
motion ; for anything like a complete study of a link-motion the 
graphic method of § 1 58 or the use of a model is to be preferred. 

160, Radial Clears. Many forms of gear for reversing and 
for varying expansion have been devised with the object of escaping 
the use of two eccentrics, and of obtaining a more perfect distri- 
bution of steam than the link-motion can in general be made to 

Fio. 94. Haokworth's Badial Valve-Gear. 

give. Hackworth s Badial gear, the parent of Several others, has 
a single eccentric E (fig. 94) opposite the crank, with an eccentric- 

1 Examples of the application of Zeuner's diagram to the link-motion will be 
found in his book on Valve-Gtears, dted above. 



Valve' PoSa 

rod EQy whose mean position is perpendicular to the travel of the 
valve. This rod ends in a block Q, which slides on a fixed inclined 
guide-bar or link, and the valve-rod receives its motion through a 
connecting rod from an intermediate point P of the eccentric-rod, 
the locus of which is an ellipse. To reverse the gear the path in 
which Q moves is tilted over to the position shown by the dotted 
lines, and intermediate inclinations give various degrees of ex- 
pansion without altering the lead. The steam distribution is 
excellent, and the cut-off is sharper than in the usual link-motion, 
but an objection to the gear is the wear of the sliding-block and 
guide. In a modified form of the Hackworth gear this objection 
is obviated with some loss of symmetry in the valve's motion by 
constraining the motion of the point Q, not by a sliding-guide as in 
fig. 94, but by a suspension- 
link, which makes the path 
of Q a circular arc instead 
of a straight line ; to reverse 
the gear the centre of sus- 
pension 12 of this link is 
thrown over to the position 
R' (fig. 95). The same 
figure (95) shows another 
modification of what is sub- 
stantially the same gear, 
namely the placing of P 
beyond Q, with no angle 
between the crank and the 
eccentric; but P may be 
between Q and the crank 
(as in fig. 94), in which 
case the eccentric is set 
at 180° from the crank. This gear, as arranged by Bremme, 
Marshall and others, has been applied in a number of marine engines. 
Another type of radial gear is Joy s, which is extensively used in 
locomotives. In Joy's gear no eccentric is required ; and the rod 
corresponding to the eccentric rod in Hackworth's gear receives its 
motion from a point in the connecting rod by the linkage shown in 
fig. 96, and is either suspended by a rod whose suspension centre R 
is thrown over to reverse the motion, or constrained, as in the original 
form of the Hackworth gear, by a slot-guide whose inclination is 

Fig. 95. 


reversed. Fig. 97 shows Joy's gear as applied to a locomotive. 
A slot-guide E is used, and it is curved to allow for the 

F aAwPott 

Fio. 96. Diagram of Joy's Valve-Gtear. 

obliquity of the valve connecting-rod AE. C is the crank-pin, 
B the line of piston's motion, and D a fixed centre. Other forms 
of radial gear, dispensing with eccentrics and more or less closely 
related to the invention of Hackworth have been designed by 
Walschaert, Morton, Brown, Bryce-Douglas, Kirk and others^ 

Fio. 97. Joy's Gear as applied to a LooomotlTe. 

A method of reversing with a common slide-valve, which 
is used in steam steering engines' is to supply steam to what 
was (before reversal) the exhaust side of the valve and connect 
the exhaust to what was the steam side. This is done by 
means of a separate reversing valve through which the steam 
and exhaust pipes pass. 

^ A disonssion of Mr Joy*8 and other arrangements will be found in Proe, Inst, 
Mech. Eng, 18S0. See also a paper by Mr J. Harrison on '* Badial Valve-Gears,'* 
Min, Proe, Inst, C, E, Vol. cxin., 1893. 

« Proe, Inst, Meek, Eng, 1867. 


161. Separate ezpansion-yalyes. When the distribution 
of steam is effected by the slide-valve alone the arc of the crank's 
motion during which compression occurs is equal to the arc 
during which expansion occurs, and for this reason the slide-valve 
would give an excessive amount of compression if it were made to 
cut off the supply of steam earlier than about half-stroke. Hence, 
when an early cut-off is wanted it is necessary either to use an 
entirely different means of regulating the distribution of steam, 
or to supplement the slide-valve by another valve, — called an 
expansion- valve, and usually driven by a separate eccentric, — ^whose 
function is to effect the cut-off, the other events being determined 
as usual by the slide-valve. Such expansion-valves belong 
generally to one or other of two types. In one, which is much 
the less common, the expansion-valve cuts off the supply of steam 
to the chest in which the main valve works. This may be done 
by means of a disk or double-beat valve (§ 167), or by means of a 
slide-valve working on a fixed seat (furnished with one or more 
ports) which forms the back or side of the main valve-chest. 
Valves of this last type are usually made in the " gridiron " or 
many-ported form to combine large steam-opening with small 
travel. Expansion-valves working on a fixed seat may be arranged 
so that the ports are either fully open (fig. 98) or closed (fig. 99) 


Seat 5— i- 


Fio. 98. Fig. 99. 

when the valve is in its middle position. In the latter case the 
expansion-valve eccentric is set in line with or opposite to the 
crank, if the engine is to run in either direction with the same 
grade of expansion. Cut-off then occurs when the crank is at P (fig. 
100), the expansion eccentric being at P', the shaft having turned 
through an angle a firom the beginning of the stroke. This is because 
the valve is then within a distance equal to I (fig. 99) of its middle 
position. The expansion- valve reopens when the crank is at Q, and 
the main slide-valve must therefore have enough lap to cut off 
earlier than 180°— a from the beginning of the stroke, in order to pre- 
vent a second admission of steam to the cylinder. In the example 
shown in fig. 100 the expansion eccentric is set at right angles 
to the crank, which is a usual arrangement when the engine is 



provided with reversing gear, since it makes the cut-oflF happen at 
the same place in the stroke for both directions of running. If 

£«p. ecoenlrie 

this condition need not be fulfilled, the expansion eccentric may 
have a somewhat diflferent angular position, and in this way a 
more rapid travel at the instant of cut-oflF may be secured for 
one direction of running. 

Since the separate expansion-valve of fig. 98 or 99 acts by 
cutting oflF the supply of steam from the steam-chest, but not 
directly from the cylinder, it does not prevent the steam which is 
stored in the chest from continuing to enter the cylinder until 
the main slide itself closes the admission port. When the cut-off 
by the expansion- valve is early and the steam-chest is capacious 
this affects the action materially. 

162. Meyer's Ezpansion-yalye. The other and much 
commoner tjrpe of expansion-valve is known as Meyer's. It 
consists of a pair of plates sliding on the back of the main 
slide-valve, which is provided with through ports which these 
plates open and close. Fig. 101 shows one form of this type. 

Fig. 101. Meyer Ezpansion-yalye. 

Here it is the relative motion of the pair of plates forming the 

expansion-valve with respect to the main-valve that has to be 

E. 16 


considered. If r^ and r^ (fig. 102) are the eccentrics working 
the main and expansion valves respectively, 
then CR drawn equal and parallel to ME 
is the resultant eccentric which determines 
the motion of the expansion-valve rela- 
tively to the main-valve. Cut-off occurs 
at Q, when the shafb has turned through 
an angle a, which brings the resultant 
eccentric into the direction CQ and makes 
the relative displacement of the two valves 

equal to the distance L Another form of this valve (corresponding 
to the fixed-seat form shown in fig. 98) cuts off steam at the inside 
edges of the expansion-slides. With the form shown in fig. 101 
the expaDsion eccentric will be set at ISO"' from the crank if the 
engine is to run in both directions with the same grade of expan- 
sion ; otherwise a somewhat different angle may often be chosen 
with advantage, as giving a sharper cut-off. 

The action of Meyer's valve may be conveniently examined by 
the help either of Zeuner's diagram or of the harmonic diagram 
of § 156. Taking Zeuner's diagram first and assuming, for greater 
generality, that the expansion eccentric is not set just opposite 
the crank, let the circles I. and II. (fig. 103) be drawn to show, 
as in fig. 82, by the length of their chords through C the amount 
of absolute displacement of the expansion slide and main slide 
respectively each from its middle position, when the crank is in 
the angular position corresponding to the direction of the chord. 
In drawing these circles the angle XCM is set out to represent 
the whole angle by which the main valve eccentric is ahead of the 
crank, as in fig. 82, and the angle XCE (also measured against 
the direction of the arrow) represents the angle by which the 
expansion eccentric is ahead of the crank, CM and CE being 
diameters of the circles II. and I. respectively. Then if any 
chord CQP be drawn from C to meet both circles the distance PQ, 
which is the difference between CP the absolute displacement 
of the main-valve and CQ the absolute displacement of the 
expansion-valve, measures the relative displacement of one with 
respect to the other. This distance PQ is equal to the chord CR 
of a third circle (III.) drawn with CF equal and parallel to EM as 
its diameter. To prove this make the supplementary construction 
shown by the dotted lines. Then since the angles at P, Q, R and 



G are right angles, being angles in semicircles, PQ equals MG in 
the parallelogram PG, and RC equals MG in the equal triangles 

Fio. 103. Application of Zenner's Diagram to the Meyer Expansion-valve. 

EMG and FCR. Hence PQ equals RC, A similar construction 
of course applies to the return stroke, for which the circle showing 
the resultant motion is III'. 

Thus by drawing the circles III. and III', we at once determine, 
by the length of their chords through C, the relative displacement 
of the two valves for all positions of the crank. Cut-off, on 
the part of the expansion-valve, occurs when the crank is in such 
a position that the chord CR is equal to I (fig. 101), which is the 
amount of relative displacement that suffices to close the steam 
passage through the main slide. The expansion-valve reopens 
when the chord is again diminished to this value, towards the end 
of the stroke, and care must be taken that the main slide has 
enough outside lap to close the steam port leading into the 
cylinder before this stage in the revolution has been reached. 

When the expansion-valve is furnished with a means of 




varying Z, as in fig. 101, the point of cut-off may be made to take 
place early or late, the limit of earliness being imposed by the 
condition that I must not be reduced below the amount which 
will give a fair steam opening and the limit of lateness being 
imposed by the consideration that the main slide itself becomes 
closed at a position determined by its own outside lap. The 
events of release, compression and admission, depending as they 
do on the main slide-valve alone are found by drawing lap arcs 
on the main-valve circle I. in the same manner as in earlier 
examples of Zeuner's diagram. 

The harmonic diagram of § 156 gives an excellent means 
of studying the action of Meyer's valve. Three distinct curves 
having been drawn for the piston, main-valve and expansion- 
valve respectively, showing the displacement of each in relation 
to the angle turned through by the crank-shaft, they are to be 

Fig. 104. 

superposed as in fig. 104 (using tracing paper as before) with 
the proper differences of angular position set out by distances 
measured along the base-line between the points at which the 
maximum displacement towards one side occurs in each. Both 
valve curves must have the same scale. Then the relative 
displacement of the valves is everywhere shown by the vertical 
distance between the main -valve curve and the expansion-valve 
curve. Cut-off is made to occur at any desired place in the 
motion by making the quantity I of fig. 101 equal to the distance 
found by measurement between the two valve curves at the 
corresponding point of the base-line. Thus in fig. 104, if it is 
wished to cut off steam when the piston has travelled 26°/^ of its 


stroke, the corresponding point P is found by projection from the 
scale at the side, PR is drawn and the intercept TR is measured : 
this determines the proper length of the ^ lap ' I, With a smaller 
'lap' the cut-off comes earlier, and in the particular example 
shown in the figure, the admission may be reduced to 10"*/^ of the 
stroke or even less by reducing L The diagram* relates to a 
case in which the expansion eccentric was set at 180"* in advance 
of the crank and the main-valve eccentric at 130"* (making = 40°). 
Both eccentrics had the same throw, giving a travel of 1'55 inches 
to each valve. The main-valve had an outside lap of 0*4 inches 
on both sides : this gave equal amounts of lead, namely 01 inches, 
but would have made the cut-off unequal on the two sides, namely 
at 70°/^, of the in-stroke or down-stroke and at 62% of the out- 
stroke or up-stroke, if the cut-off had depended on the main- valve. 
Since the cut-off is accomplished earlier, by means of the expansion- 
valve, this inequality does not matter. The inside laps of the 
main-valve were made unequal so that they should give the same 
compression on both sides, namely by stopping the exhaust at 80"*/^, 
in each back-stroke ; their values, found by projection from points 
at 80°/^, on the stroke scale were 0*24 inches on the front or 
bottom side and 0*14 inches on the back or top side. 

By measuring distances such as TR between the two valve 
curves it will be seen that equal cut-off on the two sides can only 
be secured by having different values of I at the two ends of the 
valve. Thus TR is 0*33 inches and TR, which also corresponds 
to a 257o cut-off, is 0*42 inches, or nearly one-tenth of an inch 
more. A constant difference between the values of I at the two 
ends is in fact preserved in Meyer's gear while the values of I are 
varied, and in this case the diagram shows that a constant difference 
of about one-tenth of an inch suffices to keep the points of cut-off 
practically symmetrical from say 107o *o 35% of the stroke. When 
the cut-off is to be later than 357o equality can only be preserved 
by reducing slightly the difference between the values of /. The 
difference between them can be varied in practice by shifting 
the expansion-valve bodily towards or from its eccentric, provided 
the valve-spindle in the eccentric rod be furnished with a screw 
coupling or other device which permits its length to be altered. 

The alteration of the expansion by varying the * lap ' Z is accom- 

1 Drawn by Mr W. E. Dalby for a smaU vertical experimental engine in the 
Engineering Laboratory at Cambridge. 


plished in the ordinary form of Meyer's valve in a way which will 
be evident on reference to fig. 101. The valve rod has right and 
lefb-handed screws on it working in nnts which control the 
longitudinal positions on the rod of the two blocks that make up 
the expansion-valve. Hence by rotating the rod the blocks 
are made to approach or recede from each other, thus increasing 
or reducing the lap I at each end, but leaving any difference 
between the laps at the two ends unchanged. Matters are 
generally arranged so that this adjustment can be made while the 
engine is running by means of a sleeve and hand-wheel which are 
usually fitted on a prolongation of the valve rod through the back 
end of the steam-chest. The cut-off niay also be varied by 
altering the travel of the expansion-valve, instead of its lap. In 
some examples of the Meyer gear the expansion is varied auto- 
matically to suit the varying load upon the engine, the governor 
being connected to the expansion-valve in such a way that either 
the lap or more commonly the travel is varied in response to 
variation in the speed. When the travel is to be altered a link, 
oscillating about a fixed centre, is interposed between the valve 
rod and the eccentric rod, and by sliding the end of the eccentric 
rod up or down in the link, the link is made to act as a lever 
of variable length. 

In a modified form of this valve, known as Rider's, the 
expansion-valve is a species of piston working in a cylindrical 
hole bored out of the main- valve. The steam passages terminate 
in a pair of oblique slots within this hole, and the front and^ back 
edges of the piston-shaped expansion-valve are also cut obliquely, 
with the result that when the valve is turned about its axis its 
edges approach or recede from the oblique slots which form the 
steam ports. This turning can be effected by the governor. 

163. Forms of ilide-valvei. Double-ported valve. 
Trick valve. In designing a slide-valve the breadth of the steam 
ports in the direction of the valve's motion is determined with 
reference to the volume of the exhaust steam to be discharged in 
a given time, the area of the ports being generally such that the 
mean velocity of the steam during discharge is less than 100 feet 
per second. The travel is • made great enough to keep the 
cylinder port ftiUy open during the greater part of the exhaust ; 
for this purpose it is 2^ or 3 times the breadth of the steam port. 



To facilitate the exit of steam the inside lap is always small, and 
is often wanting or even negative, especially in engines which are 
designed to mn at a high speed. Daring admission the steam 
port is rarely quite uncovered when the valve reaches the 
end of its travel, particularly if the outside lap is large and 
the travel moderate. Large travel has the advantage of giving 
freer ingress and egress of steam, with more sharply-defined 
cut-ofF, compression, and release, but this advantage is secured 
at the cost of more work spent in moving the valve and more 
wear of the faces^ To lessen the necessary travel without 
reducing the area of steam ports, double-ported valves are often 
used, and occasionally there are even three ports 
at each end An example of a double-ported 
valve is shown in fig. 106. Fig. 105 shows 
the Trick valve, a device which accomplishes 
the same purpose by giving simultaneous 
admission in two ways; steam enters directly 
past the outer edge, as in an ordinary slide- 
valve and at the same instant an opening at 
the other end of the valve is uncovered by 
passing beyond the edge of the raised seat on 
which the valve works. This gives a supple- 
mentary admission, to the same cylinder port, 
through a passage cast in the back of the 
valve itself 

Incidentally, fig. 106 illustrates an arrange- 
ment that is usual in all heavy slide-valves 
whose travel is vertical — the batance-piston, which is pressed 
up by steam on its lower side and so equilibrates the weight of 
the valve, valve-rod, and connected parts of the mechanism. 

164. Relief FrameB. To relieve the pressure of the valve 
on the seat, large slide-valves are generally fitted with what is 
called a relief-frame, which excludes steam from the greater part 
of the hsjck of the valve. In a common form of relief-frame a ring 
fits steam-tight into a recess in the cover of the steam-chest, and 
is pressed by springs against the back of the valve, which is 
planed smooth to slide under the ring. Another plan is to fit the 

1 For an experimental inyestigation of the friction of locomotive sUde-valves see 
ft paper by Mr J. A. F. Aspinall, Min. Proc. Itut. C. E. Vol. xor., 1S88. 

Fig. 106. 
Trick Valve. 



ring into a recess on the back of the valve, and let it slide on the 
inside of the steam-chest cover. Steam is in either case excluded 
from the space within the ring, any steam that leaks in being 
allowed to escape to the condenser (or to the intermediate receiver 

Fio. 107. Piston 

Fig. 106. Double-ported valve with 
balance-piston and relief-frame. 

when the arrangement is fitted to the high-pressure cylinder of a 
compound engine). A flexible diaphragm is sometimes used to 


make a steam-tight-partition between the back of the relief-frame 
and the cover of the valve-chest, and in that case the frame may 
take the form of a rectangular casting with a planed face, which 
remains at rest while the valve, the back of which is also planed, 
slides beneath it. Fig. 106 gives an example of a relief-ring fitted 
on the back of a large double-ported slide-valve for a marine engine. 

166. Piston Valves. The pressure of valves on cylinder 
faces is still more completely obviated by making the back of the 
valve similar to its face, and causing the baick to slide in contact 
with the valve-chest cover, which has recesses corresponding to 
the cylinder ports and communicating with them. This arrange- 
ment is most perfectly carried out in the piston slide-valves now 
ysrery largely used in the high-pressure cylinders of marine engines. 
The piston slide-valve may be described as a slide-valve in which 
the valve face is curved to form a complete cylinder, round whose 
whole circumference the ports extend. The pistons are packed 
like ordinary cylinder pistons by metallic rings, and the ports are 
crossed here and there by diagonal bars to keep the rings from 
springing out as the valve moves over them. Fig. 107 shows a 
form of piston valve for a marine engine. PP are the cylinder 
ports, and the supply of steam reaches the valve through two 
distinct inlets at the top and bottom. In another form of piston 
valve the rod connecting the two pistons is hollow and forms a 
communication between the steam chambers above and below the 
valve, thus making one steam inlet suffice. 

An interesting variety of the piston valve occurs in the 
Willans * central-valve ' engine to be described in a later chapter. 
In this case the piston-rod of the engine is hollow and its interior 
forms the cylindrical chamber in which the valve slides, the 
events of the distribution being determined by the relative 
movement of the main piston-rod and the piston valve within it. 

166. Rocking slide-valve. The slide-valve sometimes takes 
the form of a disk revolving or oscillating on 
a fixed seat, and sometimes of a rocking 
cylinder (fig. 108). This last kind of sliding 
motion is very usual in stationary engines 
fitted with the Corliss gear, which will be 
. more particularly described in the next chapter, Fia. 108. Booking 
in which case four distinct rocking slides are Slide-Valve. 



commonly employed to effect the steam distribution, one giving 
admission and one giving exhaust at each end of the cylinder 
(see fig. 130). A characteristic of the Corliss gear is that the 
steam valve after being held open during admission is disconnected 
from its eccentric by means of a ** trip " device, which allows it to 
close suddenly under the action of a spring. 

167. Double-beat valve. The Comiflh cataract In 

many stationary engines lift or mushroom valves are used, worked 
by tappets, cams, or eccentrics. Lift valves are generally of the 
Cornish or double-beat type (fig. 109), in which equilibrium is 

Fio. 109. Double-Beat Lift- Valve. 

secured or rather approximated to by the use of two conical 
faces of nearly the same size which open or close together. In 
Cornish pumping engines, which retain the single action of Watt's 
early engine, three double-beat valves are used, as steam-valve, 
equilibrium-valve, and exhaust-valve respectively. These are 
closed by tappets on a rod moving with the beam, but are opened 
by means of a device called a cataract, which acts as follows. 
The cataract is a small pump with a weighted plunger, discharging 
fluid through a stop-cock which can be adjusted by hand when 
it is desired to alter the speed of the engine. The weighted 
plunger is raised by a rod which hangs from the beam, but is free 
in its descent, so that it comes down at a rate depending on the 
extent to which the stop-cock is opened When it comes down a 
certain way it opens the steam and exhaust valves, by liberating 
catches which hold them closed; the "out-door" stroke then 


begins and admission continues until the steam- valve is closed; 
this is done directly by the motion of the beam, which also, at a 
later point in the stroke, closes the exhaust. Then the equi- 
librium-valve is opened, and the "in-door" stroke takes place, 
during which the plunger of the cataract is raised. When it is 
completed, the piston pauses until the cataract causes the steam- 
valve to open and the next "out-door" stroke then begins. By 
applying a cataract to the equilibrium-valve also, a pause is 
introduced at the end of the " out-door " stroke. Pauses have the 
advantage of giving the pump time to fill and of allowing the 
pump-valves to settle in their seats without shock. 

The Sulzer engines, already referred to in chapter V. (§ 119), give 
ODe out of many examples that might be cited from continental 
practice, in which the admission and exhaust are controlled by 
mushroom valves of the double-beat t3rpe. The exhaust- valves are 
placed below the (horizontal) cylinder and the admission valves 
are on the top. The latter are opened by eccentrics and are 
furnished with a trip gear which allows them to close suddenly, 
giving a sharp cut-off as in the Corliss engine^. 

^ For other examples of muBhroom valve-gears see Haeder's Handbook of the 
Steam-Engine, Tran. by H. H. P. Powles (1S93). 



168. Methods of regulating the work done in a Steam- 
engine. To make an engine run steadily an almost continuous 
process of adjustment must go on, by which the amount of work 
done by the steam in the cylinder ia adapted to the amount of 
external work demanded of the engine. Even in cases where the 
demand for work is sensibly uniform, fluctuations in boiler-pressure 
still make regulation necessary. Generally the process of govern- 
ment aims at regularity of speed ; occasionally, however, it is some 
other condition of running that is to be maintained constant, as 
when an engine driving a dynamo-electric machine is governed by 
an electric regulator to give a constant difference of potential 
between the brushes — a condition which often requires the engine 
to run rather faster when it is giving a greater output. 

The ordinary methods of regulating are either (a) to alter the 
pressure at which steam is admitted by opening or closing more or 
less a throttle-valve between the boiler and the engine, or (6) to 
alter the volume of steam admitted to the cylinder by varying the 
point of cut-off. The former plan was introduced by Watt and is 
still common, especially in small engines. From the point of view 
of heat economy it is somewhat wasteful, since the process of 
throttling is irreversible in the thermodynamic sense, but this 
objection is lessened by the fact that the wire-drawing of steam 
dries or superheats it, and consequently reduces the condensation 
which it suffers on coming into contact with the chilled cylinder 
walls. On the other hand, to hasten the cut-off does not 
involve a reduction of efficiency unless the ratio of expansion is 
already very great. The second plan of regulating is in general 



Fio. 110. Watt*B 

to be preferred, especially when the engine is subject to large 
variations of load, and is usually followed in stationary engines 
of the larger types. 

169. Automatic regulation by centrifligal speed go- 
Temors. Watt's Conical Pendulum Governor. Within 
certain limits regulation by either plan can be eflfected by hand, 
but for the finer adjustment of speed some form of automatic 
governor is necessary. Speed governors are commonly of the 
centrifugal type : a pair of masses revolving 

about a spindle which is driven by the 

engine are kept from flying out by a 

certain controlling force. When an increase 

of speed occurs this controlling force is no 

longer able to keep the masses revolving in 

their former path ; they move out until the 

controlling force is sufficiently increased, 

and in moving out they act on the regulator 

of the engine, which may be a throttle- valve 

or some form of automatic gear by which 

the cut-off is varied. In the conical pendulum governor of 

Watt (fig. 110) the revolving masses are balls attached to a 

vertical spindle by rods, and the controlling force is furnished 

by the weight of the balls, which, in receding from the spindle, 

are obliged to rise. When the speed exceeds or falls short of its 

normal value they move out or in, and so raise or lower a collar C 

which is in connexion with the throttle-valve through a lever. The 

suspension-rods may be hung from the ends of a T-piece attached 

to the revolving spindle instead of being pivoted in the axis as in 

fig. 110, and in some cases they cross each other and the spindle 

itself as in fig. 122, 

170. Loaded Governors. In a modified form of Watt's 
governor, known as Porter's, or the loaded governor, the tendency 
which the balls have to fly out is resisted not only by their own 
weight but also by a supplementary controlling force which is 
furnished by a weight resting on the sliding collar (fig. 111). This 
device is equivalent to increasing the weight of the balls without 
altering their mass. In other governors the controlling force 
instead of being due to gravity only is wholly or partly produced 


by springs. Fig. 112 shows a governor by Messrs Tangye in 

Fia. 111. Loaded Ck>vemor. Fio. 112. Spring Governor (Tangye). 

which the balls are controlled partly by their own weight and 

Fia. 118. Spring Governor (W. Hartnell). 


partly by a spring, the tension of which is regulated by turning 
the cap at the top. Another example of a governor with spring 
control is shown in fig. 113, There the balls move in a sensibly 
horizontal line and consequently their weight contributes nothing 
towards resisting the tendency to fly out. A certain amount 
of additional control, however, is supplied by the weight of the 
sliding collar and the parts which rise with it, unless these are 

171. Controlling Force. In whatever way the tendency 
of the balls to fly out be resisted, whether through their own 
weight or through a supplementary load or through springs, it is 
convenient to treat the control as equivalent to a certain force F 
acting on each ball in the direction of the radius towards the axis 
of revolution. We shall call this the controlling force. The value 
of F varies, in a given governor, when the position of the balls 
changes. If it were not for friction, the controlling force for any 
position of the balls could be found experimentally by appljdng a 
spring-balance to each ball, with the governor at rest, and noting 
the force required to hold the ball in the assigned position when 
this force was applied directly away from the axis of the governor. 
Owing to friction such an experiment would give two extreme 
values of the force, for if the pull on the spring-balance were 
increased the ball would not move further out until the pull 
became equal to F+f, where / denotes the influence of friction. 
And if the effect of friction in resisting the return of the ball were 
the same as its effect in resisting the displacement outwards, the 
pull of the spring-balance might be reduced to -F— /before the 
ball would begin to move in. A mean of these extremes would 
give the true controlling force in cases where the influence of 
friction remained unchanged. 

When the governor is running the influence of friction is in 
general less than when it is at rest ; but the effect still is to make 
the actual force which the ball experiences, pulling it towards the 
spindle, greater or less than F according as the ball is on the 
point of moving out or moving in. 

172. Condition of Equilibrium. Once the controlling force 
F is known the speed at which the governor must revolve in order 
to make the balls take up any assigned position is readily calcu- 
lated. If if be the mass of the ball (in lbs.), n the number of 



revolutions per second and r the radius (in feet) of the path in 
which the balls revolve, equilibrium will be maintained when 

F, the controlling force, being expressed in poundals. Hence the 
speed corresponding to the assigned configuration of the governor 
is defined by the equation 

^'iirV Mr' 

For the present, friction is left out of account; its influence on the 
speed will be considered immediately. 

173. Condition of Stability, A governor is said to be 
stable when (apart from the influence of friction) any small finite 
increase or decrease of speed above or below the speed proper to 
any given configuration makes the balls go out or come in by a 
finite amount, so that they reach a new position of equilibrium 
corresponding to the new speed. 

In order that a governor should be stable F must increase 
more rapidly than r when the balls move outwards. That is to say. 

This follows, by the above equation, from the 

fact that the new position of the balls is to correspond to a greater 
value of the speed n. 

If F varied just proportionally to r, n would be constant for all 
values of r. This state of things would correspond to neutral 
equilibrium on the part of the governor: its consequences are 
considered more particularly in § 176 below. 

174. Equilibrium of the Conical Pendulum Governor. 
Height of the Governor. When the governor is a simple 

hF ^ .8r 

-= must exceed — 
Jf r 

Fig. 114. 

Fig. 115. 

Fig. 116. 

conical pendulum controlled by gravity only and without load 
other than the weight of the balls themselves — a condition never 


quite realised in practice, since the weight of the sliding collar and 

its attached parts always applies some extra load 

which adds to the controlling force — F is the 

resultant of F^ the tension in the suspending rod 

and F^ or Mg the weight of the ball (figs. 114 — 

116). The triangle of forces is sketched in fig. 

117. This applies whichever of the three forms 

shown in figs. 114, 115, and 116 is given to the 

governor. Let the hmghJb of the pendulum 

governor, that is the vertical distance from the 

plane of rotation of the balls to the point where 

the axis of the suspending rod (produced if 

necessary) cuts the axis of the spindle, be called A. Then, 

using absolute units for the forces, 

bom which 


Hence in a governor of this type, the condition of stability 
may be expressed by saying that A must diminish when the 
speed increases. This will obviously happen if the form be that of 
fig. 114 or fig. 115. With the crossed-rod form of fig. 116 the height 
h will increase when the balls rise only if the points of suspension 
are not far from the axis. By placing them at a particular distance 
from the axis, h may be kept very nearly constant: in other 
words, this governor may be arranged to have nearly neutral 
equilibrium, so that a very small change in the speed n may be 
associated with a large change in the position of the balls. When 
the centres of suspension are put further from the axis the 
mechanism sketched in fig. 116 becomes unstable, and is then unfit 
to serve as a governor. 

176. Eqiilllbrium of Loaded Gk>vemor. The results 
obtained in the last paragraph are readily adapted to the case of 
a governor of the Porter type (fig. 111). Let W be the amount 
of the extra load, per ball, and let q be the velocity ratio of the 
vertical movement of the load to the vertical movement of the 
ball — ^a quantity which is easily found by calculation or graphically 
when the form of the governor is given. Then each ball, in being 
displaced outwards, has not merely to raise its own weight but has 
E. 17 



to raise what is equivalent to an additional weight equal to q 
times the weight of Jf . The effect of the load is therefore to 

increase the controlling force F from — ^ , in poundals, to 


But the condition of equilibrium still is that F should be equal to 
47r^'rJlf. Hence the speed n at which the governor must now 
turn to maintain any assigned height h is 

1 /(M+qAr)g 

Compared with the simple or unloaded form, this governor requires 
a higher speed in the proportion of VJIf + qM' to »JM, 

In the ordinary construction of the Porter governor the four 
links form a parallelogram and consequently the vertical move- 
ment of the load borne by the sliding collar is twice that of the 
balls, or g = 2. And as the whole load is divided between two 
balls, each ball virtually has its weight, but not its mass, increased 
by an amount equal to the whole weight of the central load. 

Fig. 118. 

Another way of considering the equilibrium of the Porter 
governor may be mentioned. Let the mass of each ball be M and 
let that of the load be 2M' as before. The load, the weight of 
which is 2M^g in poundals, is borne by the tensions in the two 
lower rods (fig. 118). By drawing the triangle abc which is 
the diagram of forces for the load and in which ab or F^ia the 
weight of the load, we find the value of F^ and jP/ which are the 
tensions in the lower rods. Then draw bd or ^i to represent the 
weight of one ball (namely Mg), and draw the horizontal line 


de to meet a line C6 drawn from c parallel to the direction of 
the upper rod. The figure ecbd is the polygon of forces acting 
on the ball, ed being the resultant controlling force F. The 
speed at which the governor will run is determined by the con- 
dition that 4rn^^M is to be equal to this force ed. In the usual 
case of parallel rods, ace is one straight line and then 

ed=:ad tan a, or F=(M'\- 2M')g tan a, 

where a is the inclination of the rods to the vertical. Since 

tan (i = T this expression agrees with the one given above. 

176. Sensibility in a Ck>vemor. Xsochronism. Any 

change of speed in a governor tends to produce a change in the 
position of the balls, and if the governor itself and the regulating 
mechanism connected with it were free from friction only one 
position of the governor would be possible for any one speed, 
provided the condition of stability were complied wif h. If therefore 
the supply of steam depends on the position taken up by the 
governor balls a stable governor does not maintain a strictly 
constant speed in the engine it controls. Whenever the boiler 
pressure or the demand for work changes a certain amount of 
displacement of the balls is necessary to increase or reduce the steam 
supply, and the balls can retain their new position only by virtue 
of continuing to turn slower or faster than before. The maxi- 
mum change of speed which can occur under the control of the 
governor is that which will make the balls move from one to the 
other extremity of their range — ^namely from the position which 
allows the full supply of steam to the position which completely 
checks the supply. Of course if the engine is overloaded by giving 
it too much external resistance to overcome, the speed may be 
further reduced after the governor has done all that it can do 
to let steam in freely, but the variation of speed for which the 
governor is responsible is only that which makes the change from 
no steam to full steam. When a small variation of speed suffices 
to do this the governor is said to be sensitive, its sensibility being 
measured by the ratio which this variation of speed bears to the 
mean speed. 

The more stable a governor is the less sensitive is it ; on the 
other hand when the equilibrium is neutral the sensibility is 



indefinitely great. The controlling force F then varies as r, 
and hence n is constant (§ 172) at whatever distance from the axis 
the balls revolve. In other words, the balls are in equilibrium at 
one speed and only at one (except for friction), and the least 
variation from, this speed suffices to send them to one extremity or 
the other of their range. A governor having this quality is said 
to be isochronous. Friction makes the condition of strict iso- 
chronism impossible, but many governors are made nearly iso- 
chronous by arranging them so that, as the balls are displaced, 
the controlling force increases only a little more rapidly than r. 

177. Xsochronism in the Gravity Governor. Parabolic 
Governor. An ideal frictionless governor, in which the con- 
trolling force is frimished by gravity, can be made isochronous 
if the balls instead of being hung by rods from fixed points are 
constrained to move in a parabolic path, as in fig. 120, where the 
cup or channel which holds the ball is so shaped that the locus of 

Fig. 120. 

the centre of the ball, shown by a dotted curve, is a parabola. The 
pressure of the ball against the cup is equivalent to the tension 
of an imaginary suspension rod PQ ; and it is a property of the 
parabola that the sub-normal QM, which represents A, is constant 
wherever P be taken along the curve. Hence a ball supported 
in this way would remain in equilibrium at one particular speed 
of rotation on the part of the cup, but would fly up to the rim 
of the cup if the speed were ever so little increased, and would 
sink to the foot if the speed were ever so little reduced. 

Fig. 121 shows a practical form of parabolic governor^ An 

1 From Mr J. Head's paper on ** A Steam-engine Governor,'* Proc, ImU Mech, 
Eng, 1871. 



important feature is the air-cylinder at the top, forming a dash- 
pot, which is famished, with a small adjustable orifice through 

Fio. 121. Parabolio Gk)yemor. 

which air is driven out or in as the balls rise or fall The function 
of this is to check the tendency which the balls have to hunt 
(§ 183 below), or to fly violently in or out when the speed drops 
below or rises above the normal value, 

178. Approzimate Isochronism in Pendulum Ck>vernors. 

A useful approximation to the condition of isochronism can be 
reached in the conical pendulum governor by using crossed rods 
with the centres of suspension at a suitable distance from the 
axis. K each centre of suspension were so placed as to be at the 
centre of curvature of a parabolic arc which coincided, at the 
position corresponding to the normal speed, with the actual circular 
curve along which the balls rise and fell, the governor would be 
sensibly isochronous at that speed. By taking points a little 
nearer the axis for the two centres of suspension a margin of 
stability, always necessary in practice, is secured, but the governor 
is left nearly enough isochronous to be very sensitive. This 
crossed-rod type of governor, which is due to Farcot, is often 



met with in a loaded form. An example is given in fig. 122- 
Loading a governor (whether the rods are crossed or open) need 

Fig. 122. Loaded GoTernor with Crossed IBMb, 

not aflfect the sensibility ; it makes a higher speed necessary, but 
the proportion of the fluctuation of speed to the mean speed is 
not changed, provided the links are arranged in such a way that 
the vertical velocity-ratio of the load and the balls does not alter 
as the balls rise. 

Another approximately isochronous form of gravity governor 
is Proll's (fig. 128), which is interesting as exemplifying a diflferent 

Fig. 123. Pr6ll*8 Governor, 
method of reducing the stability of the pendulum type. Let the 
ball be supported not at the joint between the links as in the 
ordinary Porter governor but at the end of an arm projecting 
upwards and rigidly connected to the lower link. By a proper 


choice of the length of this arm the controlling force may be made 
as nearly proportional to the radius as may be desired. 

Pendulum governors of the stable class are occasionally loaded 
indirectly, the weight which forms the load being applied at some 
point in the lever by which the governor is connected with the 
valve. This allows the load and therefore the speed to be adjusted: 
further, by applying the load at the end of a cranked arm in the 
lever in such a way that it becomes less eflfective when the balls 
go out, the system can be made approximately isochronoua 

179. Gtovemon with spring control. Adjustment of 
sensitiveness. When springs furnish the conti*olling force, in 
whole or part, as in the governors shown in figs. 112 and 113, their 
tension is generally adjustable. This gives a convenient means of 
altering the speed ; at the same time it affects the sensitiveness of 
the governor. In spring governors which are constructed so that 
the radial displacement of the balls produces a proportional 
change in the tension of the spring, the condition of isochronism 
can be approached, as nearly as may be wished, by giving the 
spring a suitable amount of initial tension. Thus in Mr Hartnell's 
apparatus, fig. 113, where the balls move in a nearly horizontal 
direction and gravity has almost nothing to do with the control, 
the governor can be made isochronous by screwing down the 
spring so that the initial force exerted by the spring (before the 
balls are displaced) is to the increase of this force by the dis- 
placement of the balls, as the initial radius of the balls' path is to 
the increase of that radius by the displacement. This makes F 
proportional to ?*, and therefore requires no change in n as the 
balls move out. Any greater initial tension would make the 
governor unstable, and a less tension is in fact necessary, in order 
that the sensitiveness may not be impracticably great. 

180. Determination of the Controlling Force. Whatever 
be the method of control, by weights or springs or both, the control- 
ling force F may generally be calculated for any assumed position 
of the balls. The simple pendulum governor both unloaded and 
loaded as in fig. Ill has already been considered. A case such as 
that of fig. 112 or fig. 113 presents no difficulty when the stiffness 
and initial tension of the spring are given. Slightly less. simple 
cases of the loaded governor present themselves when the balls 
are not placed at the joints between the upper pair of links and 



Fio. 124. 

the lower pair which carry the load. Let the ball M (fig. 124) be 
fixed on the upper link AB, at any place either beyond B or 
between A and B. First find ^i, the stress 
in BO, firom the consideration that BC and its 
twin link on the other side are in simple 
tension and support between them the load. 
Then the forces acting on ABM, namely 
Fi, the tension in BC, F^ which is the weight 
of the ball, and F which is the force to be 
determined, are in equilibrium, and hence F 
is readily found by taking moments about A. 
We here treat F as the equilibrant instead 
of the resultant of the forces which are actually 
applied, for the sake of bringing the system into static equilibrium. 
When the ball is carried by the link BC or by a piece rigidly 
connected to it as in PrblFs governor we 
may proceed thus (fig. 125): — The forces 
concerned in the equilibrium of the rigid 
piece CBM are (1) F^ the half weight of 
the load acting at C, which is the vertical 
component of the pull at the joint C, (2) the 
horizontal component J^4 of the pull at the 
joint G, (3) the tension F^ in the link AB^ (4) 
the weight of M, or F2, and finally (6) the 
force F which is to be determined. The 
resultant of F^ and J^4 no longer acts along 
BC for there is a bending moment on the 
piece CBM, Compound F^ and F^ into a single force F^. 
Since F^ and F are horizontal, this vertical force F^ 
must be wholly balanced by the vertical component of 
the stress in ^S. Hence F^ is found by drawing a 
right-angled triangle (fig. 126) with a line parallel to 
AB as h3rpotenuse and with a vertical side equal 
to F^, Having found F^ we are in a position to take 
moments about C in order to find F, which is now the Fio. 126. 
only unknown force not acting through (7. 

181. Influence of Friction. Power of the Gk>vemor. 

We may express the influence of friction on the behaviour of a 
governor by treating it as equivalent to a force with some 


limiting value /, acting radially on each ball, in the same 
direction with the controlling force F when the balls are moving 
out and in the opposite direction when they are moving in. This 
makes the whole controlling force -P+/ in the former case and 
jP— / in the latter. Let n be the speed proper to the force F 
alone, then if there were no friction any increase of speed above n 
would begin to alter the configuration, making the .balls move 
out ; but in consequence of friction this does not happen until the 
speed has increased by some finite amount An such that 

Similarly, should the speed fall below the normal speed n 
proper to any configuration, friction prevents the balls from 
beginning to move in until the reduction of speed A'n is such 


Mr • 

Hence in consequence of friction the speed may alter as much 
as An above and A'n below the normal speed n, while the position 
of the balls remains unchanged. From the above equations, if 
An be small relatively to n as it alwajrs should be in practice, we 
have, approximately, 

n tF' 

This variation of speed due to friction is independent of whatever 
further variation of speed the governor may allow in consequence 
of its equilibrium being stable (§ 176), and would of course be 
experienced even with a governor which except for friction was 

To keep the eflfects of friction within moderate limits it is 
essential that F should be great in comparison with / The 
fiictional resistance / proceeds partly from the joints of the 
governor itself but mainly frx>m the throttle-valve spindle or from 
the expansion gear the position of which the governor has to 
regulate. A powerful governor, namely a governor with a large 
amount of controlling force F^ is therefore required when any 
considerable amount of frictional resistance in the valve or 
gearing is to be overcome. With simple pendulum governors, the 
only way to secure power in this sense is to make the balls large. 



Loaded governors have the advantage that great power may be 
secured with comparatively small revolving masses. The quality of 
powerfulness in a governor is increased whenever the controlling 
force is increased, whether by gravity loading or by the use of 
springs. From another point of view, the loaded governor (with 
the same revolving masses) is more powerful because it runs at a 
higher speed ; but this is just because its controlling force F is 

182. Gunres of Controlling Force. The consideration of 
sensitiveness and powerfulness in governors generally is greatly 
elucidated by using a graphic method, suggested by Mr Hartnell^, 
of exhibiting the controlling force. Having found F for various 
positions of the balls, let a curve PiPj (fig. 127) be drawn in which 

A, A Aa 

Radius of PaiKr, 

Fio. 127. Carve of Controlling Foroe. 

abscissae represent r the radius of the balls' path and ordinate^ 
represent F. To find the configuration proper to any assigned speed 
n draw a line OS at such an inclination that tan SOX = 49r*n*ilf , 
due regard being had to the scales of F and r. When the base 
OX is taken equal to unity on the scale used in plotting r, the 
value of SX is equal to 4i7rWM on the scale used in plotting F 
Let P be the point in which this line cuts the curve of F. Then 


F^PA = OAtajx POA = 47r»iiVJf, 

it follows that the point of intersection P determines the radius 

OA at which the governor will run when the speed is n. Similarly 

the tangent of the angle which is made with the base by any other 

1 Proc, Inst MecK Eng, 18S2. 



line drawn from to meet the curve, such as OPi or OP^, is 
proportional to the square of the speed at the corresponding path- 
radius OAi or OA2. Thus if OAi be set off to represent the least 
and OA2 the greatest radius, corresponding to the positions giving 
full steam and no steam respectively, the inclinations of the lines OPi 
and OPt determine the whole range through which the speed will 
alter in consequence of the stability of the governor (apart fix)m 
any effect of friction). 

Further, if a pair of additional curves QiQ, and RiR^ be drawn 
as in fig. 128 to represent the values of jF+/and -P— /respectively, 
in relation to r, the diagram shows 
the additional changes of speed 
that are due to friction. The 
lowest possible speed is then de- 
termined by the inclination of 
the line ORi, the highest by that 
of the line OQ2. 

Again, the whole work done 
in altering the configuration of 
the governor, while the balls move 
out from Ai to A2 would be 
(for each ball) equal to the area 
AiPiPjiAi if there were no fric- 
tion to be overcome : actually it 
is the area AiQiQ^A^. And as 

the ball comes in frx)m A^ to Ai the part of the stored energy 
which is recovered is measured by the area AJR^RiAi, the rest 
having been spent on friction. The area PiQiQ^P^ is the work 
spent against friction while the governor is closing the throttle- 
valve or shifting the expansion gear from full steam to no steam. 

The powerfrilness of the governor is measured in a definite 
manner by the area AiPiP^^, namely the work stored and 
restored (save for friction) as the governor balls open or close 
throughout their range. In order that friction should cause no 
very serious irregularity in speed this area must be many times 
greater than the area P1Q1Q2P3 or P^PJlJli. These last areas 
are equal if the friction / has the same value in closing as 
in opening the valve, but the construction shown in fig. 128 is 
evidently applicable whether / has or has not the same value 
during the rise and &I1 of the balls. 

Fio. 128. Curves of Controlling Force, 
taking friction into account. 


Again, the governor is stable provided the inclination of the 
curve to the axis OX be greater than the inclination of a line 
drawn from to meet the curve at any point within the range 
of possible positions. Thus in fig. 127 the curve shows the governor 
to be stable because any line OP is less steep than the inclination 
of the curve itself at P. This is the condition of stability stated 
in § 178, namely that the controlling force must increase more 
rapidly than the radius. A strictly isochronous governor would 
have for its curve of F and r a straight line passing, when 
produced, through 0. If this condition were fulfilled by the 
line without friction P1P2, the line with friction Q^Q^ which 
lies above PiP^ at a more or less constant distance from it would 
in general be less steep than a line from drawn to meet it, 
which would mean that friction would make the otherwise neutral 
governor unstable. This is one reason why an isochronous 
governor is impracticable. The governor of fig. 128 is stable 
notwithstanding friction. 

183. Hunting. Apart from the reason just stated it is in- 
dispensable to give a governor some margin of stability, especially 
when the influence of the regulator takes much time to be felt by 
the engine. An over-sensitive governor is liable to fall into a state 
of oscillation called hunting. When an alteration of speed begins 
to be felt, however readily the governor alters its form the engine's 
response is more or less delayed. The action of the regulator does 
not immediately take full effect upon the speed in consequence 
of the energy that is stored within the engine itself, not only in 
its moving parts but also in the steam that has passed the regu- 
lator and is still doing work in the engine. If the governor acts 
by closing a throttle-valve, the engine has still a capacious valve- 
chest on which to draw for steam. If it acts by changing the cut- 
off, its opportunity has passed if the cut-off has already occurred, 
and the control only begins in the next stroke. This lagging 
of effect is specially felt in compound engines, where that portion 
of the steam which is already in the engine continues to do its 
work for nearly a whole revolution after passing beyond the 
governor's control. The result of this storage of energy in an 
engine whose governor is too nearly isochronous is that whenever 
the demand for power suddenly falls the speed rises so much as 
to force the governor into a position of over-control, such that the 


supply of steam is no longer adequate to meet even the reduced 
demand for power. Then the speed slackens, and the same kind 
of excessive regulation is repeated in the opposite direction. A 
state of forced oscillation is consequently set up. The effect is 
aggravated by the momentum which the governor balls acquire 
in being displaced, and also, to a very great degree, by the friction 
of the governor and the regulating mechanism. There is hunting 
due to friction, hunting due to the momentum of the governor 
itself, and hunting due to the storage of steam. Hunting is to 
be avoided by giving the governor a feir degree of stability, by 
reducing as far as possible the static frictional resistances, and by 
introducing a visc(ms resistance to the displacement of the go- 
vernor, which prevents the displacement from occurring too 
suddenly, without affecting the ultimate position of equilibrium. 
For this purpose many governors are furnished with a dash-pot, 
which is a hydraulic or pneumatic brake, consisting of a piston 
connected to the governor, working loosely in a cylinder which is 
filled with oil or with air. An instance of the use of a dash-pot 
has already been mentioned in speaking of the parabolic governor 
of fig. 121. 

184. Governor with horizontal aids. In some high-speed 
engines the governor balls or blocks instead of revolving about a 
vertical axis are arranged about the main shaft of the engine. 

Fio. 129. Governor of Armington & Sime Engine. 

sometimes within the fly-wheel, the control being given by springs. 
An example is shown in fig. 129, which is the governor of the 


Armington and Sims engine. Here the govempr produces auto* 
matic variations of the cut-off by acting on the main slide- 
valve of the engine (there being no separate expansion-valve). 
The displacement of the revolving masses Jf, M changes both the 
throw and the angular advance of the eccentric, thereby effect- 
ing a change in the steam supply similar .to that produced by 
"notching up" a link-motion. The eccentricity B is altered by 
the relative displacement of two parts G, D into which the eccentric 
sheave is divided. This relative displacement not only changes 
the length of B but gives it more or less of angular advanced 
Governors resembling that of fig. 129 are often set on a horizontal 
axis in small high-speed engines. 

185. Throttle-valve and automatic expansion -gear. 

The throttle-valve, as introduced by Watt, was originally a disk 
turning on a transverse axis across the centre of the steam-pipe. 
It is now usually a double-beat valve (fig. 109) or a piston-valve. 
When regulation is effected by varying the cut-off, and an expan- 
sion-valve of the slide-valve type is used, the governor generally 
acts by changing the travel of the valve. Fig. 113 illustrates 
one usual mode of doing this, by giving the expansion valve its 
motion from an eccentric rod through a link the throw of which is 
varied by the displacement of the governor balls. In some forms 
of automatic expansion gear the governor acts upon the lap of 
the expansion valve. In others it acts by shifting the expansion 
eccentric round upon the shaft and so changing its angular advance. 
In others, again, it acts on an ordinary slide-valve through some 
form of link-motion or in such a way as has just been described. 

186. Corliss and other Trip-gear. In large stationary 
engines the most usual plan of automatically regulating the 
expansion is to employ some form of trip-gear, the earliest type 
of which was introduced in 1849 by G. H. Corliss of Providence, 
U.S. In the Corliss system the valves which admit steam are 
distinct from the exhaust-valves. The latter are opened and 
closed by a reciprocating piece which takes its motion from an 
eccentric. The former are opened by a reciprocating piece, but 
are closed by springing back when released by a trip- or trigger- 
action. The trip occurs earlier or later in the piston's stroke 

^ For other governors of a like kind see Mr HartneU's paper cited above. 



according to the position of the governor. The admission-valve 
is opened by the reciprocating piece with equal rapidity whether 
the cut-oflf is going to be early or late. It remains wide open 
during the admission, and then, when the trip-action comes into 
play it closes suddenly. The indicator diagram of a Corliss engine 
consequently has a nearly horizontal admiBsion-line and a sharply 
defined cut-oflf. Generally the valves of Corliss engines are 




cylindrical plates turning in hollow cylindrical seats which extend 
across the width of the cylinder. Often, however, the admission- 



valves are of the disk or double-beat type, and spring into their 
seats when the trip-gear acts. Many forms of Corliss gear have 
been invented by Corliss himself and by others. One of these, 
the Spencer Inglis^ trip-gear, by Messrs Hick, Hargreaves & Co., 
is shown in figs. 130 and 131. A wrist-plate A, which turns on a 
pin on the outside of the cylinder, receives a motion of oscillation 
from an eccentric. It opens the cylindrical rocking-valve B by 
pulling the link C, which consists of two parts, connected to each 
other by a pair of spring clips a, a. Between the clips there is a 
rocking-cam b, and as the link is pulled down this cam places 
itself more and more athwart the link, until at a certain point it 
forces the clips open. Then the upper part of the link springs 
back and allows the valve B to close by the action of a spring in 
the dash-pot D, When the wrist-plate makes its return stroke 
the clips re-engage the upper portion of the link (7, and things 
are ready for the next stroke. The rocking-cam b has its position 
controlled by the governor through the link E in such a way that 
when the speed of the engine increases it stands more athwart 
the link (7, and therefore causes the clips to be released at an 

Fig. 131. Corliss Valve-gear, Spencer Inglis form. 

earlier point in the stroke. A precisely similar arrangement 
governs the admission of steam to the other end of the cylinder. 
The exhaust-valves are situated on the bottom of the cylinder, at 
the ends, and take their motion from a separate wrist-plate which 
oscillates on the same pin with the plate A\ 

1 Proc. Inst, Mech, Eng. 1868. 

^ Numerous forms of Corliss gear are illustrated in W. H. Uhland's work on 
Corliss engines, translated by A. Tolhausen (London, 1879). 



Fig. 132 shows a compact form of trip-gear by Dr ProU. A 
rockiDg-lever ah is made to oscillate on a fixed pin through its 

Fio. 132. — PrdU's Automatic Expansion Gear. 

centre by a connexion to the crosshead of the engine. When the 
end a rises, the bell-crank lever c engages the lever d, and when a 
is depressed the lever d is forced down and the valve e is opened 
to admit steam to one end of the cylinder. As a continues 
moving down a point is reached at which the edge of c slips past 
the edge of d, and the valve is then forced to its seat by a spring 
in the dash-pot /. This disengagement occurs early or late 
according to the position of the fulcrum piece g, on which the 
heel of the bell-crank c rests during the opening of the valve. 
The position of ^r is determined by the governor which is of the 
kind already mentioned in § 178. A similar action, occurring at 
the other end of the rocking-bar ah, gives steam to the other end 
of the cylinder. In one form of ProlFs gear both ends of ah act 
on the same steam-valve, which is then a separate expansion-valve 
fixed on the back of a chest in which an ordinary slide-valve 

E. 18 



187. Dlfengagemeiit govemon. In the ordinary form of 
centrifugal governor the position of the throttle-valve, or the 
expansion-link, or the Corliss trigger depends on the configuration 
of the governor, and is definite for each position of the balls. In 
disengagement governors, of which the governor A shown on the 
right-hand side in fig. 133 is an example, any reduction of speed 

Fio. 183. Knowles'B tiupplementary Governor. 

below a certain value sets the regulating mechanism in motion, 
and the adjustment continues until the speed has been restored. 
This is done by means of the wheel c which comes into gear with 
a wheel on the end of the spindle a when the speed falls below 
a certain limit. Similarly a rise of speed above a certain limit 
sets the regulating mechanism in motion in the other direction by 
putting b in gear with a. If the spindle a is connected to the 
regulator so as to give more steam when it turns one way and less 
when it turns the other, the speed at which the engine will run 
in equilibrium must lie between narrow limits, since at any speed 
high enough to keep b in gear with a the supply of steam will go 
on being reduced, and at any speed low enough to bring c into 
gear with a the supply will go on being increased. This mode of 
governing, besides being sensibly isochronous, has the important 
advantage that the power of the governor is not limited by the 
controlling force on the balls, since the governor acts by applying 
a portion of the power that is being developed by thd engine to 
the work of moving the regulator. It is rarely applied to steam- 



engines, mainly because its action is too slow. This defect has 
been ingeniously remedied in the supplementary governor of Mr 
W. Knowles, who has combined a disengagement governor with 
one of the ordinary t3rpe in the manner shown in fig. 133 ^ Here 
the spindle a, driven by the supplementary or disengagement 
governor A, acts by lengthening the rod d which connects the 
ordinary governor B with the regulator. It does this by turning 
a coupling nut e which unites two parts of d, on which right- and 
left-handed screws are cut. Any sudden fluctuation in speed is 
immediately responded to by the ordinary governor. Any more 
or less permanent change of load or of steam-pressure gives the 
supplementary governor time to act. It goes on adjusting the 
supply until the normal speed is restored, thereby converting the 
control of the ordinary governor, which is stable, and therefore not 
isochronous, into a control which is isochronous as regards all 
fluctuations of long period. The power of the combination, how- 
ever, is limited to that of the ordinary governor B. 

188. Relay governors. Other governors which deserve to 
be classed as disengagement governors are those in which the 
displacement of the governor affects the regulator, not directly 
by a mechanical connexion, but by admitting steam ot other fluid 
into what may be called a relay cylinder, whose piston acts on the 
regulator. In order that a governor of this class should work 
without hunting, the piston and valve of the relay cylinder should 
be connected by what is termed differential 
gear, the effect of which is that for each 
displacement of the valve by the governor 
the piston moves through a distance propor- 
tional to the displacement of the valve. An 
example of differential gear is shown in 
fig. 134*. Suppose that the rod a is connected 
with the governor so that it is raised by an 
acceleration of the engine's speed. The rod o 
which leads from the relay piston b to the 
regulator serves as a fulcrum, and the valve- 
rod d is consequently raised. This admits 
steam to the upper side of the piston and 
depresses the piston, which pulls down d with 

Fia. 134. Differential 
Gear for Belay 

1 Proe. Inst, Mech. Eng, 1884. 



it, since the end of a now serves as a fulcrum. Thus by the 
downward movement of the piston the valve is again restored 
to its middle position and the movement of the regulator then 
ceases until a new change of speed occurs. A somewhat 
similar differential contrivance is used in steam-steering engines 
to make the position of the rudder follow, step by step, every 
movement of the hand-wheeP; also, in the steam reversing 
gear which is applied to large marine engines, to make the 
position of the drag-link follow that of the hand-lever; and 
also in certain electrical governors^ The effect of adding a 
differential gear such as this to a relay governor or other dis- 
engagement governor is to convert it from the isochronous to the 
stable type. 

189. Differential or dsrnamometric governors. Another 
group of governors is best exemplified by the "differential" 
governor of the late Sir W. Siemens' (fig. 
135). A spindle a driven by the engine drives 
a piece b (whose rotation is resisted by a 4| ^^- fp=^€^ 
Mction brake) through the djmamometer 
coupling c, consisting of a nest of bevel-wheels 
and a lever d which is loaded, the weight of 
the load acting at right angles to the plane 
of the paper. So long as the speed remains ' ^®°^®^* 

constant the rate at which work is done on 
the brake is constant and the lever d is steady. If the speed 
increases, more power has to be communicated to 6, partly 
to overcome the inertia and partly to meet the increased 
resistance of the brake, and the lever d is displaced. The lever d 
works the throttle-valve or other regulator, either directly or by a 
steam relay. The governor is isochronous when the force em- 
ployed to hold d in position does not vary ; if the control of d is 
arranged so that the force tending to hold it in position increases 
when d is displaced, the governor is stable. A governor of this 
class may properly be called a dynamometric governor, since it 
regulates by endeavouring to keep constant the rate at which 
energy is transmitted to the piece 6. In one form of Siemens's 

1 See a paper by Mr J. Mao Farlane Gray, Proc. Inst. Mech, Eng, 1867. 
' Willans, Min, Proc, Inst, C.E,, Vol. lxxxi. p. 166. 
5 Proc. Inst. Mech, Eng, 1863. 


governor the friction-brake is replaced by a sort of centrifugal 
pump, consisting of a paraboloidal cup, open at the top and 
bottom, whose rotation causes a fluid to rise in it and escape over 
the rim when the speed is suflSciently great. Any increase in the 
cup's speed augments largely the power required to turn it, and 
consequently affects the position of the piece which corresponds 
to d,^ Siemens's governor is not itself used to any important 
extent, but the principle it embodies finds application in a number 
of other forms. 

The "velometer" or marine-engine regulator of Messrs Durham 
and Churchill^ is a governor of the same t3rpe. In it the rotation 
of a piece corresponding to 6 is resisted by means of a fan 
revolving in a case containing a fluid, and the coupling piece 
which is the mechanical equivalent of d in fig. 135 acts on the 
throttle-valve, not directly but through a steam relay. In Silver's 
marine governor' the only friction-brake that is provided to resist 
the rotation of the piece which corresponds to 6 is a set of 
air- vanes. The inertia is, however, very great, and any accelera- 
tion of the engine's speed consequently displaces the dynamometer 
coupling, and so acts on the regulator in its effort to increase the 
speed of b. 

Another example of the differential type is the Allen governor *, 
which has a fen directly geared to the engine, revolving in a case 
containing a fluid. The case is also free to turn, except that it is 
held back by a weight or spring and is connected to the regulator. 
So long as the speed of the fen is constant, the moment required 
to keep the case from turning does not vary, and consequently the 
position of the regulator remains unchanged. When the fan turns 
fester the moment increases, and the case has to follow it (acting 
on the regulator) until the spring which holds the case fr*om 
turning is sufiiciently extended, or the weight raised. The term 
*' dynamometric governor " is equally applicable to this form ; the 
power required to drive the fan is regulated by an absorption- 
dynamometer in the case instead of by a transmission-dynamo- 
meter between the engine and the fen. In Napier's governor 
the case is fixed, and the reaction takes place between one 
turbine-fen which revolves with the engine and another close to it 

1 Proc. Itut. Meek. Eng, 1866; or PhiL Trans. 1866. 

» Proc. Intt, Meek, Eng. 1879. • Bnt. Aas. Rep. 1869, p. 123. 

* Proc. Inst. Mech. Eng. 1893. 



which is held from taming by a spring and is connected with the 

190. Pump govemon. Pump governors form another group 
closely related to the diflTerential or dynamometric type. An 
engine may have its speed regulated by working a small pump 
which supplies a chamber from which water or other fluid is allowed 
to escape by an orifice of constant size. When the engine quickens 
its speed the fluid is pumped in faster than it can escape, and the 
accumulation of the fluid in the chamber may be made to act on 
the regulator through a piston controlled by a spring or in other 
waya This device has an obvious analogy to the cataract of the 
Cornish pumping-engine (§ 167), which has, however, the some- 
what, different purpose of introducing a regulated pause at the 
eud of each stroke, or rather serves this purpose in addition to 
regulating the number of strokes per minute. The '* differential 
valve-gear " invented by Mr H. Davey, and successfully applied by 
him to modem pumping-engines, combines the ftmctions of the 
Cornish cataract with that of a hydraulic governor for regulating 
the expansion ^ In this gear, which is shown diagrammatically in 
fig. 136, the valve-rod of the engine (a) receives its motion from a 

Fig. 136. Davey's Differential Valve-Gear. 

lever b, one end of which (c) copies, on a reduced scale, the 
motion of the engine piston, while the other end (d), which forms 
the fulcram, has its position regulated by attachment to a sub- 

1 Proe. Intt. Mech, Eng, 1874. 


sidiary piston-rod, which is driven by steam in a cylinder e, and is 
forced to travel at a nearly uniform rate by a cataract/ The point 
of cut-off is determined by the rate at which the main piston over- 
takes the cataract piston, and consequently comes early with light 
loads and late with heavy loads. 

191. Governing marine engines. The government of 
marine engines is peculiarly difficult on account of the sudden and 
violent fluctuations of load to which they are subjected by the 
alternate uncovering and submersion of the screw in a heavy sea. 
However rapidly the governor responds to increase of speed by 
closing the throttle- valve, an excess of work is still done by the 
steam in the valve-chest and in the high-pressure cylinder. To 
check the racing which results from this, it has been proposed to 
supplement the control which the throttle-valve in the steam- 
pipe exercises by throttling the exhaust or by spoiling the 
vacuum. With the same object Messrs Jenkins and Lee have 
given supplementary regulation by causing the governor to open 
a shunt-valve connecting the top with the bottom of the low- 
pressure cylinder, thus allowing a portion of the steam in it to 
pass the piston without doing work. In Dunlop's pneumatic 
governor^ an attempt is made to anticipate the racing of the 
screw by causing the regulator to be acted on by the changes of 
pressure on a diaphragm which is connected by an air-pipe with 
an open vessel fixed under the stern of the ship. A plan has 
been used on small steamers by Mr W. B. Thompson to prevent 
the racing of the engines by working the valves from a lay shaft 
which is driven at a uniform speed by an entirely independent 
engine. So long as this lay shaft is not driven too fast the main 
engine is obliged to follow it ; if the lay shaft is driven faster 
than the main engine can follow the main engine pauses so as 
to miss a stroke, and then goes on. Reversing the motion of the 
lay shaft reverses the main engine. 

1 Proc. Inst. Meek. Eng, 1S79. 



192. Fluctuations of Speed during any single revolu- 
tion : ftinction of the Fly-wheel. Besides those variations of 
speed which occur from stroke to stroke, which it id the business 
of the governor to check, there are variations within each single 
stroke over which the governor exercises no control. These are 
due to the varying rate at which work is done on the crank- 
shaft during its revolution. To keep them within reasonable 
limits is the function of the fly-wheel. It acts by forming a 
reservoir of energy to be drawn upon during those parts of the 
revolution in which the work done on the shaft is less than the 
work done by the shaft, and to take up the surplus in those parts 
of the revolution in which the work done on the shaft is greater 
than the work done by it. To accomplish this alternate storing and 
restoring of energy the fly-wheel has to undergo slight fluctuations 
of speed, whose range depends on the ratio which the alternate 
excess and defect of energy bears to the whole stock of energy the 
fly-wheel holds in virtue of its motion. The duty of the fly- 
wheel may be studied by drawing a diagram of crank-effort, 
which shows the work done on the crank in the same way that 
the indicator diagram shows the work done on the piston. The 
same diagram serves another useful purpose in determining the 
twisting and bending stress in the crank 

193. Diagram of crank-effort. The diagram of crank- 
effort is best drawn by representing, in a curve drawn with rect- 
angular co-ordinates, the relation between the torque or moment 
which the connecting-rod exerts to turn the crank and the angle 



turned through by the crank. When the angle is expressed in 
circular measure, the area of the diagram is the work done on the 
crank. Or instead of selecting the turning moment and the angle 
turned through as the two co-ordinates, we may take the tangential 
effort on the crank-pin as one coordinate, namely the force which 
is found when the thrust against the crank-pin is resolved along 
the tangent to the crank-pin's path, the other component being 
directed towards the centre of the crank-shaft and consequently 
exerting no turning moment. The linear motion of the crank-pin 
in its circular path is then taken as the other co-ordinate of the 
crank-effort diagram ; and the area still represents the work done 
upon the crank. 

Neglecting friction for the present, and supposing in the first 
place that the engine runs so slowly that the forces required for 
the acceleration of the moving masses are negligibly small, the 
moment of crank-effort is found by resolving the thrust P of the 
piston-rod into a component Q along the connecting-rod and a 

Fig. 137. 

component normal to the surface of the guide (fig. 137). The 
moment of crank-effort is 

Q-aJf = P-(7JV^ = Prsina(H" 


VP — r* sin« a 


where GIf is drawn perpendicular to the centre line or travel of 
the piston, r is the crank, I the connecting-rod, and a the angle 
ACB which the crank makes with the centre line. A graphic 
determination of GNia the most convenient in practice, unless the 
connecting-rod is so long that its obliquity is negligible, when the 



second term in the above expression vanishes. Fig. 138 shows the 
diagram of crank-effort determined in this way for an engine 

01 334567 89 10 11 
Angle turned fry erank 

Fio. 138. Diagram of Crank-Effort. 

whose connecting-rod is 3^ times the length of its crank, and in 
which steam is cut off at about one-third of the stroke. The 
thrust P is determined from the indicator diagrams of fig. 137 by 
taking the excess of the forward pressure on one side of the piston 
over the back pressure on the other side, and multipljdng this 
effective pressure by the area of the piston. The area of the 
diagram of crank-effort is the work done per revolution. 

In the example for which this diagram is drawn it happens 
that there is very little compression 
of steam at the end of each back 
stroke, and consequently the forward 
pressure is greater than the back 
pressure throughout the whole of 
the stroke. In many cases, however, 
the back pressure rises so much toward 
the end of the stroke that the resul- 
tant thrust on the piston opposes its 
motion, the diagram of resultant steam 

pressure taking a form such as that sketched in fig. 139, and 
consequently the ordinates in the corresponding part of the 
crank-effort diagram become negative. 

194 Effect of Friction. The friction of the piston in the 
cylinder and the piston-rod in the stuflSng-box is easily allowed 
for, when its amount is known, by making a suitable deduction 
from P. Friction at the guides, at the cross-head, and at the 
crank-pin has the effect of making the stress at each of these 
places be inclined to the rubbing siufaces at an angle if>, the angle 
of repose, whose tangent is the coefficient of friction. Hence the 
thrust of the guide upon the cross-head instead of being normal 
to the surface of the guide, is inclined at the angle if> in the 

Fig. 189. 


direction which resists the piston's motion (fig. 140) ; and the 
thrust along the connecting-rod, instead of passing through the 
centre of each pin, is displaced far enough to make an angle if> 
with the radius at the point where it meets the pin's surface. To 
determine this displacement of the line of thrust let a " friction- 
circle " be drawn about the centre of each pin, namely a circle 
with radius equal to p sin ^, where p is the actual radius of the 
pin. Any line drawn tangent to this circle will make the angle ^ 
with the radius of the pin at the surface of the pin and will there- 
fore satisfy the required condition as regards friction. The thrust 
of the connecting-rod must be tangent to both circles ; it must 
therefore be drawn as in fig. 140, so that it resists the rotation of 
the pins relatively to the rod. The direction of rotation of the 
pins is shown by curved arrows in the figure, where the friction- 



















circles are drawn to a greatly exaggerated scale. Finally, P (after 
allowing for the friction of piston-packing and stuflSng-box) is re- 
solved into and Q, and then Q • CM, the moment of Q on the 
shaft, is determined. This gives a diagram of crank-effort, correct 
so far as friction affects it, whose area is no longer equal to that of 
the indicator diagram. The difference, however, does not repre- 
sent the whole work lost through friction in the mechanism, since 
the friction of the shaft itself, and of the valves and other parts 
of the engine which it drives, has still to be allowed for if the 
frictional eflSciency of the engine as a whole is in question. 

195. Effect of the inertia of the reciprocating pieces. 

The diagram of crank-effort is further modified when we take 
account of the inertia of the piston and connecting-rod, and the 
influence of inertia is generally much more important than that of 


firictioiL For the purpose of investigating the effects of the 
inertia of the reciprocating pieces, we may assume that the crank 
is revolving at a sensibly uniform rate of n turns per second. Let 
M be the mass of the piston, piston-rod, and cross-head in pounds, 
and a its acceleration at any instant in feet per second per second, 

the force required to accelerate it is — , in pounds- weight, and 


this is to be deducted in estimating the effective value of P. The 
effect is to reduce P during the first part of the stroke and to 
increase it towards the end, thereby compensating to some extent 
for the variation which P undergoes in consequence of an early 
cut-off. If the connecting-rod is so long that its obliquity may be 
neglected the piston has simple harmonic motion, and 

a = — 47r'n*r cos a, 

when the crank has turned through any angle a from its dead point. 
More generally, whatever ratio the length I of the connecting-rod 
bears to that of the crank r, 

rl^ cos 2a -I- r* sin* a\* 

V (?-?•» sin' a)* 

* To prove this, let 6 be the angle BAG of fig. 137 ; then 

. , /r sin a\ 

*=""-' (-1-)- 

do r 008 a da 2imr cos a 

. ^ , / ri^co8 2a-l-r'sin*a\* 
a = — 47r'nV(cosaH 1 — I . 


^^ Jt^-i^^n^adt Jl^-r^Bin^a' 

Differentiating again, and remembering that -^^=0 since the rotation is 

assmned to be sensibly uniform, we obtain 

d^0^ -r(Za-rg)sina (day_ - Ar^nh {I^ - r^) sin a 
^^^ (l^-f^Bin^a)^ \^^) (ia-r»8in2o)* 

Again, writing xiox AC (fig. 137) 

a;=rcosa + icos^, 
dx . da , , ^d$ 


a^x /day , ^fde\^ , - ^^^ 

Substituting the values found above for :^ , ^ and 3:^ * ^^ patting r sin a for 

at at at^ 

loose and JP-r^Bin^a for I cos $ this gives the expression in the text, 

>i_2 2- / . rPcos2tt +r»sin<a \ 

a= -4iH/iV ( oosa + r~ )• 

\ (P-r8sinao)t / 



The effect is to make, on the diagram of P, a correction of the 
character shown in fig. 141 where the broken line cd refers to the 
case of an indefinitely long connecting-rod and the fall line aeb to 
the case of a connecting-rod 3J times the length of the crank. 
In a vertical engine the weight of the piston and piston-rod is to 
be added to or subtracted fi:om P. 

The form of the inertia line aeb of fig. 141 may be determined 
much more shortly and with sufficient accuracy for any graphic 
application by finding the points a and e and b as follows, and 
then sketching a smooth curve through these three points. The 
position of the point e in the stroke is found from the fact that 
since the acceleration is then zero the velocity of the piston is a 
maximum : this happens when the crank and connecting-rod are 
at right angles. The acceleration at a is the ^centrifugal 
acceleration due to the sum of the curvatures of the path of the 

Fig. 141. 

Fig. 142. 

crank-pin and of the arc A A' struck with I for radius (fig. 142). 
Similarly the acceleration at b (fig. 141) is due to the difference 

of these curvatures. Hence at a the acceleration is -- -|- -^ where 

r I 

V is the velocity of the crank-pin, and at 6 it is j. Sub- 
stituting 27mr for v in these expressions the acceleration of the 
piston is found to be 

47r^V (l -h i) and 47r^V (l - j\ 
at a and b respectively. 

196. Inertia of the Connecting-rod. To allow for the 
inertia of the connecting-rod is a matter of somewhat greater 
difficulty. A rough approximation to the real effect may 
be arrived at by supposing part of the whole mass of the rod 


to be gathered at the cross-head, forming an addition to the 
mass which has a simply reciprocating motion, and the remainder 
to be gathered at the crank-pin, forming an addition to the 
rotating mass of the fly-wheel. To obtain an exact solution the 
motion of the rod may be analysed as consisting of translation 
with the velocity of the cross-head, combined with rotation about 
the cross-head as centre. By means of this analysis, the force 
required for the acceleration of the rod is determined as the 
resultant of three components, namely, Fi, the force required 
for the linear acceleration a (which is the same as that of 
the piston); jP,, the force required to cause angular accelera- 
tion about the cross-head ; and F^, the force towards the centre 
of rotation, which depends on the angular velocity, and is 


Fio. 148. 

eqiial and opposite to the so-called centrifugal force. Let 6 as 



before be the angle BAG (fig. 143), so that -^ is the angulgtr 

d^0 . 
velocity of the rod about il,and -p- is its angular acceleration, and 

let M' be the mass of the rod. Then, using gravitational units, 

and acts through the centre of gravity G', parallel io AG; 

„ MXAQ) d^0 
9 de' 

and acts at right angles to the rod through the centre of per- 
cussion H; 

„ M'jAO) fd0\' 

^* — r~\dt)' 

and acts along the rod towards A. 

J/} J2/3 

The values of a and of j- and -rr. in relation to the crank 

dt dt^ 

angle a have already been given, in the foot-note to § 195. 


Having calculated these forces we have to find their moments 
about G and then to deduct the sum of their moments from the 
turning moment on the crank as found without reference to the 
inertia of the connecting-rod, before proceeding to draw the 
crank-efifort diagram. 

The weight of the rod as well as its resistance to acceleration 
should be taken account of. To do this the weight is to be 
treated as a single force acting vertically through and exerting 
a moment about G which is to be added to or subtracted fi'om the 
turning moment according as it helps or opposes the rotation. 

197. Treatment of Inertia and Friction together. 

When in addition to the inertia of the rod, the friction at the 
cross-head and crank-pin is to be taken account of, the whole group 
of forces acting on the rod may be considered as follows. Com- 
pound forces equal and opposite to Fi, F^, and F^ into a single 
force R (fig. 144), which may be called the resultant resistance to 

Fig. 144. 

acceleration of the connecting-rod. If the weight of the rod is to 
be considered, let it also be taken as a component in reckoning R, 
Then the rod may in any position be regarded as in equilibrium 
under the action of the forces Q, R and 8, where Q and 8 are the 
forces exerted on it by the cross-head and crank-pin respectively. 
These three forces meet in a point p in the line of action of R, 
which point is to be found by trial, the 
condition being that in the diagram of 
forces, fig. 145, after the triangle POQ 
has been drawn, and the force jB set out, 
the force-line 8 shall be parallel to a line 
drawn from p tangent to the friction- 
circle of the crank-pin, as shown in fig. 144. When this condi- 



tion has been satisfied by trial, the value of 8^ which is the thrast 
on the crank-pin, is determined, and then 8 . CM is the moment 
of crank-eflFort. This method is due to Fleeming Jenkin, who 
applied it with great generality to the determination of the 
fiictional efficiency of machinery in two important papers ^ the 
second of which deals in detail with the dynamics of the steam- 
engine. Fig. 146, taken &om that paper, shows the diagram of 

Fig. 146. 

crank-eflFort in a horizontal direct-acting engine, — the full line 
with friction, and the dotted line without friction, — the inertia 
of the piston and connecting-rod being taken account of, as well 
as the weight of the latter. It exhibits well the influence which 
the inertia of the reciprocating parts exerts to equalize the crank- 
effort in the case of an early cut-off. The cut-off is supposed to 
occur pretty sharply at about one-sixth of the stroke. The engine 
considered is of practical proportions, and makes four turns per 
second ; and the initial steam pressure is 50 lb. per square inch. 
It appears from the diagram that, with a slightly higher speed, 
or with heavier rods, a better approach to uniformity in the crank- 
effort might be secured, especially as regards the stroke towards 
the crank, which comes first in the diagram ; on the other hand, 
by unduly increasing the mass of the reciprocating pieces or their 
speed the inequality due to expansion would be over-corrected 
and a new inequality would come in. 

In drawing crank-effort diagrams it is seldom necessary in 
practice to take account of the friction of the guide and of the 
pins, but the inertia of the piston, piston-rod and connecting-rod 

1 Transactions of the Royal Society of Edinburgh, Vol. xxvra, p. 1 and p. 703. 



is of the utmost importance, especially in high-speed engines. 
The graphic method which is exhibited in figs. 144 and 145 
of finding S, the thrust on the crank-pin, after R the resistance to 
acceleration of the connecting-rod has been determined, may of 
course be as readily applied when firiction is neglected as when it 
is taken into account. 

198. Forms of Crank-Effort Diagrams. When two or 
more cranks act on the same shaft the joint diagram, showing the 
resulting turning moment, is found by combining the separate 
diagrams of crank-effort for the several cranks. An example is 
shown in fig. 147 where the dotted lines are the separate diagrams 

12 3 4 5 6 7 8 9 10 11 12 
Fig. 147. Crank-EfiEort Diagram for Two Cranks. 

for two cranks set at right angles to each other and the full line is 
the combined diagram. It is obvious that the inequalities of 
crank-effort are vastly reduced by using two cranks instead of 
one, and with three cranks the effort becomes still more uniform. 
An illustration of this is given in fig. 148 which also exemplifies 
the circular form in which the diagram of crank-effort is sometimes 
drawn. In this construction lines proportional to the moment are 
set off radially from a circular line which represents the zero of 
moment. The figure is one drawn by Kirk for a triple-expan- 
sion marine engine with three cranks at 120° from each other. 
The curves show the resulting crank-effort, as determined from 
actual indicator diagrams and as affected by the inertia of the 
reciprocating parts. They are drawn for various numbers of 
revolutions per minute, which are indicated by the distinguishing 
numbers, the line marked referring to an indefinitely slow 

As' an opposite extreme to the nearly uniform crank-effort that 
is obtained by the use of three cranks the case may be named of an 
explosive gas or oil engine using the " Otto " cycle in which under 
E. 19 



the most favourable conditions the whole effective action on the 
crank takes place only in one single stroke out of two revolutions 

Fia. 148. Circular Diagram of Crank-Effort for a Three-Cylinder Engine. 

(or four strokes), two of the other three strokes being idle and the 
third being that in which the explosive mixture is compressed 
before ignition (see § 240 below). The student will find it a 
useful exercise to draw a crank-effort diagram for such a case, 
extending the diagram over two revolutions to get a complete 
cyclic period, and then to apply the method described below of 
determining the size of fly-wheel which is necessary to prevent 
the speed from fluctuating beyond assigned limits. 

199. Fluctuation of Speed in relation to the Energy of 
the Fly-wheeL The extent to which the fly-wheel has to act 
as a reservoir of energy is found by comparing the diagram of 
effort exerted on the crank-shaft by the piston or pistons with a 
similar diagram drawn to show the effort exerted by the crank- 
shaft throughout the revolution, in overcoming the resistance of 
the mechanism which it drives as well as the resistance due 
to its own frictioa Like the driving effort, this resistance 
may be expressed as a torque or moment, or (dividing the 


moment by the radius of the crank) we may state the equivalent 
resistance referred to the crank-pin as a force acting always 
tangent to the crank-pin's path. In general, except in such cases 
as are offered by direct-acting pumping and blowing engines. 

Fig. 149. 

the resistance may be taken as having a constant moment on 
the shaft, and the diagram of effort exerted by the crank-shaft 
is then a straight line, as EFOHIJKL in fig. 149. At F, 0, H, 
/, J, and K the rate at which work is being done on and by 
the shaft is the same; hence at these points the fly-wheel is 
neither gaining nor losing speed. The shaded area above FG 
is an excess of work done on the crank, and raises the speed 
of the fly-wheel from a minimum at -P to a maximum at Q, 
From GtoH the fly-wheel supplies the defect of energy shown 
by the shaded area below QH, which represents the amount by 
which the demand for work exceeds the supply ; the speed of the 
wheel again reaches a minimum at H, and again a maximum 
at /. The excesses and defects balance in each revolution if 
the engine is making a constant number of turns per second. 
In what follows it is assumed that they are only a small 
fraction of the whole energy stored up by the fly-wheel in virtue 
of its revolution and consequently that the variations in speed 
are small in comparison with the mean speed. In practice 
the dimension and speed of the fly-wheel are chosen so that this 
is the case : indeed the chief object of the investigation is to find 
what amount of energy must be given to the wheel in order that 
the variations in speed may not exceed a prescribed range. 

Let ^E be the greatest single amount of energy that the fly- 
wheel has to give out or absorb, which is determined by measuring 
the shaded areas of the diagram and selecting the greatest of these 
areas; and let Wi and o), be the maximum and minimum values 
of the wheel's angular velocity, which occur at the extremes of 
the period during which it is storing or supplying the energy AE. 



The mean angular velocity of the wheel a>o will be sensibly equal 
to i(a)i4-a)j) if the range through which the speed varies is 
moderate. Let Eo be the energy of the fly-wheel at this mean 
speed. Then 

where / is the moment of inertia of the fly-wheel. Also 

The quantity -^^ ', which we may write q, is the ratio of the 

extreme range of speed to the mean speed, and measures the 
degree of unsteadiness which the fly-wheel leaves uncorrected. If 
the problem be to design a fly-wheel which will keep q down to 
an assigned limit, the energy of the wheel must be such that 

The periodic fluctuations of speed which are due to the limited 
capacity the fly-wheel has for storing energy may be examined 
experimentally by means of the familiar chronographic device of 
causing a vibrator, such as a tuning fork electrically maintained 
in vibration, to scribe its oscillations on a surfece which moves with 
the fly-wheel shaft. A sheet of smoked paper clasping the shaft 
itself forms a convenient surface, on which the fork draws an 
undulating line by means of a bristle or light pointed spring 
attached to one of its prongs. The fork should be mounted 
on a carrier such as the slide-rest of a lathe so that it may 
be kept moving slowly in a direction parallel to the axis of the 
shaft, in order that the records of successive revolutions may be 
traced on fresh portions of the smoked surface*. 

200. Reversal of thrust at the Jointa Prevention of 
reversal of the thrust in single-acting engines. Let the 

diagram of resultant steam thrust upon the piston be represented 
by the line 8S as in fig. 150 for the two successive strokes 
of a revolution, the line being drawn in such a way as to show 

I For examples of the use of this method of finding q see Mr H. B. Bansome's 
paper, Min. Proc. InsU C, E, Vol. xcvin., or the Society of Arts Report on Triali 
of Motors for Electric Lighting (1889). 



that the steam is pushing the piston towards the crank when it 
lies above the base, and is pulling the piston away from the crank 

Fig. 160. 

when it lies below the base. Let the line RR represent in the 
same way the forces that are used up in producing the accelera- 
tion of the reciprocating pieces. Then the points at which the 
steam curve 88 crosses the inertia curve BR mark the places 
at which the direction of thrust at the bearings becomes reversed. 
If in drawing RR the mass of the piston, piston-rod and cross- 
head only is taken account of the intersection of the two curves 
will show at what places the thrust changes its sign at the cross- 
head pin. But if the mass of the connecting-rod also has been 
added in calculating the forces represented by this curve, the 
points where S>S» crosses RR will relate to the reversal of 
thrust on the bearing surfaces of the crank-pin. Two inertia 
lines may be drawn, one referring to the masses between the 
steam and the cross-head pin, the other to the whole reciprocating 
mass, up to the crank-pin. Since the bearings are necessarily 
somewhat loose to admit of lubrication and free turning of the 
pins in their brasses, a sudden reversal of the thrust from pull 
to push at either joint will give rise to a knock. To prevent an 
engine from knocking badly the clearance at the bearings is of 
course to be kept as small as possible and the form of the thrust 
diagram (fig. 150) has to be such that when the steam and inertia 
curves cross each other the change from positive to negative in 
the distances intercepted between them shall be gradual. 

In some forms of high-speed single-acting engines this change 
is entirely avoided, and in that case the bearings may be left slack. 
In the Willans engine for example the back is the active end and 


the piston and connecting-rod are kept in compression throughout 
the revolution. During the stroke towards the crank this is their 
natural state, except when the speed is so great as to make the point 
a of fig. 141 rise above the steam thrust line. But during the 
out-stroke there is nothing happening in the cylinder, except a 
little compression towards the end of the stroke, to provide the force 
that is required to reduce the velocity of the reciprocating pieces 
after the point of maximum velocity (near mid-stroke) has been 
passed. Hence unless special provision for this force were made 
the connecting-rod would be pulling instead of pushing the crank- 
pin during the later portion of the out-stroke. In the Willans 
engine the special provision consists in an air-cylinder, the piston 
of which is arranged tandem with the steam piston (or steam 
pistons, in the case of a tandem compound engine of this single- 
acting class). The air in this cylinder begins to be compressed 
early in the out-stroke and becomes more and more compressed 
to the end, the energy which is expended in compressing it 
being given out again during the in-stroke or eflFective stroke of 
the engine. The force exerted by the compressed air is arranged 
to be always in excess of the force that is required for the 
(negative) acceleration of the pistons and rods, and hence the 
thrust both at the cross-head and at the crank-pin is con- 
tinuously a push, never a puU^ 

201. Balancing. An important matter in the kinetics of 
the steam-engine is the balance of its working parts. A machine 
is said to be perfectly balanced when the relative movements 
of its parts have no tendency to make it vibrate as a whole. In 
other words, perfect balance implies that the reactions of those forces 
that are required for the acceleration of the parts neutralize each 
other in every phase of the motion, so that no resultant reaction 
is ever felt by the bed-plate of the machine. A perfectly balanced 
machine would be self-contained as regards the stresses between 
the parts and would nin steadily without foundations. Actual 
machines rarely do more than approximate to this condition. 

In steam-engines and other machines using a piston, connecting- 
rod and crank, an approximate balance can be attained, so far as 
forces parallel to the direction of the stroke are concerned, by 

^ See Discussion on High-Speed Motors, Min. Proe, Inst. C. E, Vol. Lxmn., 


connecting to the crank-shaft two or more masses which revolve 
with it and are arranged so that the radial forces required to 
accelerate them are together equal and opposite to the force 
required to accelerate the piston, piston-rod, connecting-rod and 
crank-pin when the piston is at its dead-point. A single revolving 
mass is insufficient to effect this balancing, for it cannot be placed 
just opposite the crank-pin, and if placed alongside it still leaves 
an unbalanced couple the moment of which tends to rock the 
bed-plate about an axis perpendicular to the stroke and to the 
axis of the shaft. By using a pair of masses this is avoided. 
In the figure (fig. 151) AB is the axis of the shaft and CO is the 

aI 7 •"^« 





Fio. 151. 

direction of the stroke. The reciprocating pieces are treated as a 
single mass M concentrated at the crank-pin, the effective length 
of the crank to the centre of the pin being r. Let balancing 
masses Mi and M^ be set opposite the crank with their centres of 
gravity at distances n and r^ respectively from the axis of the shaft. 
Then to avoid having any resultant centrifugal force parallel to 
CO the condition must hold that 

MiTi -h M^r^ = Mr, 

And to avoid any centrifugal couple tending to twist the machine 
about an axis perpendicular to the plane of the figure, 


In an engine with a single crank the balance masses M^ and M^ 
are generally made equal and placed symmetrically on the two 
sides of the crank. 

A balance arrived at in this way is not perfect, even as regards 


forces parallel to the direction of the stroke. The assumption 
that the whole reciprocating mass M might be treated as if it 
were collected at the crank-pin is more and more wide of the 
truth the shorter the connecting-rod is. With a short rod there 
is, as we have seen above, an important difference at the two 
dead-points in the values of the force necessary for accelerating 
the reciprocating parts. Hence at one dead-point (namely when 
the piston is nearest to the crank) the force due to the balance- 
weights are in excess, and at the other dead-point they are in 
defect, of the force that has to be balanced. The treatment of 
the whole reciprocating mass as if it were collected at M is 
equivalent to ignoring the shortness of the connecting-rod. 

With this reservation a balance may be secured ia respect 
of forces acting in the plane of the sketch (fig. 151), namely the 
plane containing the line of stroke and the axis of the shafb, and 
all that has beeu said above relates to forces in that plane only. 
As regards forces at right angles to that plane the piston and 
piston-rod require no balancing for they suffer no acceleration at 
right angles to the plane in question, and only a part of the con- 
necting-rod can be taken as approximately sharing the crank-pin's 
motion in this respect. Hence the balancing masses which have 
been calculated for the forces in the plane GO A will be altogether 
excessive in respect of forces in the direction normal to that and 
will give rise to vibrations in other directions. The conditions 
that are necessary to secure a balance in the two planes are incom- 
patible, and the best results will in general be arrived at by a 

In machines that can be anchored down to a massive founda- 
tion a state of defective balance only results in straining the parts 
and causing needless wear and friction at the crank-shaft bearings 
and elsewhere, and in communicating some tremor to the ground. 
The problem of balancing is of much more consequence in loco- 
motive engines, where any bad want of balance produces oscil- 
lations that might be dangerous. 

In locomotives the existence of two cranks adds a slight 
complication to the problem of determining proper balance-weights 
to avoid horizontal oscillations; and this of course applies generally 
to engines with more than one crank. Let M, M' be the masses 
of the reciprocating parts referred to the crank- pins. Suppose 
that the balancing masses are to be carried (as is usual) on the 



driving wheels A and B, To balance M alone would require two 
masses namely Mi on A and M3 on B, placed opposite to M and 
satisfying the conditions that 

MiVi + M^Vi = Mr, 

and Jl/in AP = M^r^ BR 

Similarly to balance M^ alone would require 
two masses, Jf/ on A and M2 on JB, placed 
opposite to M and satisfying two corres- 
ponding conditions. 

For the two balancing masses on each 
wheel there may then be substituted a single 
.nass on each wheel occupying a position 
between the two, but nearer to Mi on wheel 
A and nearer to ifj on wheel B. Here again, 
owing to the incompatibility of vertical with 
horizontal balance a compromise is desirable, 
and the final adjustment of the balancing 
masses is usually a matter of experiment, the 
locomotive being hung in chains to allow its 
oscillation to be observed. 

Fig. 162. 


— ■ M 

■P " ■ 

' J 

- - M] 




202. Heating 8uillu)e5 in Boiler and Feed-water Heater. 

In the transfer of energy from fuel to steam two stages may be 
distinguished. First, the potential energy of combustion is trans- 
formed into actual heat, which shows itself in the raised tempera- 
ture of the furnace gases ; and, second, the heat of the furnace 
gases passes by conduction through the heaiing surface into the 
water of the boiler. The furnace gases serve as a vehicle for the 
conveyance of heat from the furnace or fire-box where it is 
generated to the various parts of the heating surface, some of 
which may be a long way from the actual seat of combustion. 
The heating surface is made, up of the surface of the furnace 
or combustion-chamber, so far as that is brought into contact with 
the water, and of the flues or tubes through which the hot gases 
pass on their way to the chimney. The effectiveness of any 
portion of the heating surface depends mainly on the difference in 
temperature between the gases on one side and the water on the 
other, and on the freedom with which steam, when formed, can 
escape from the surface. Differences in specific conductivity and 
in thickness of metal affect the result less than might be expected, 
partly on account of the resistance which is offered to the passage 
of heat through the scale which forms on the metallic surface, 
but mainly because the steam that is generated on the surface itself 
opposes the conduction of heat and must give place to unevapo- 
rated water before much more heat can be taken in. 

As the gases traverse the flues or tubes their temperature 
falls, until they finally escape at a temperature which is necessarily 


somewhat higher than that of the water to which they have been 
yielding up their heat. This temperature, however, is not 
necessarily the temperature of the steam, for after ceasing to be in 
contact with the boiler proper the gases may continue to give up 
heat to 8k feed'Watet^ heater, which is a set of pipes through which 
the comparatively cold feed-water passes on its way to the boiler. 
The feed- water heater virtually forms an extension of the heating 
surface, with the advantage that it is more eflfective for the 
transfer of heat than an equivalent extension of the boiler surface 
proper would be, on account of the lower temperature of the 
contents ; and it allows the initial temperature of the feed- water, 
instead of the temperature of the steam, to form the lower limit to 
which the temperature of the gases might conceivably be allowed 
to fall. Conduction however would become so slow if the tempera- 
ture of the gases approached this limit that in practice they are 
always considerably hotter. Even after passing a feed-water 
heater, the gases rarely have a temperature less than 400° Fah. 
When the draught through the fire is maintained by means of 
a chimney there is this independent reason for allowing the gases 
to escape at a relatively high temperature that the draught 
depends on the contents of the chimney being lighter than the 
air outside, and this lightness is secured by their being consider- 
ably hotter than the atmospheric air. 

203. Draught. The furnace gases are made up of the 
products of combustion along with a quantity of air of dilution 
which passes through the furnace without undergoing chemical 
change. For the complete combustion of each pound of coal 
about 12 pounds of air are required to furnish the necessary 
oxygen, and usually about 12 pounds more have to enter as air of 
dilution. The greater part of this air enters through the grate, 
between the fire-bars on which the burning fuel rests, but some 
air has to be admitted above the fire to complete the burning 
of the combustible gases. This is specially necessary when fresh 
coal is thrown on the fire and volatile hydrocarbons are being given 
off. The furnace door has apertures to allow a small pcurt of the 
air to pass through it, and these are often made adjustable in area. 

A natv/ral or chimney draught is one which is produced 
wholly by the lightness of the contents of the chimney. A forced 
draught is one in which other means are taken to produce a 


difference between the pressure of the air inside and outside of 
the furnace. A fan, for instance, may be used to force the draught, 
either by extracting air from the flues or by blowing air into 
a closed room from which the furnace takes its supply. Or a jet of 
steam may be made to blow in the chimney, producing a partial 
vacuum there on the principle of the jet pump. 

With a forced draught it is easy to produce much more 
difference in pressure above and below the grate than can readily 
be produced by means of a chimney, and consequently to compel 
the entrance of a larger quantity of air through the fuel, with 
the result that a much larger quantity of coal can be burned per 
square foot of grate. A furnace using chimney draught does not 
as a rule bum more than 20 lbs. of coal per hour per square 
foot of grate, but with forced draught the combustion may go on 
at four or five times this rate and still be fairly perfect. 

Further, when the draught is forced the combustion is intensi- 
fied and localised, and it is found that a smaller proportion of air 
will suffice for dilution. Instead of the 24 lbs. or so of air which 
chimney draught requires per lb. of coal, 18 lbs. or less will serve. 
Hence with a forced draught the temperature of the furnace gases 
is higher, and consequently the effectiveness of the heating 
surface is increased. Again, since the proportion of air passing 
through the furnace is reduced by forcing the draught, the 
proportion of heat lost in the hot gases is also reduced, provide 
the heating surface be extended sufficiently to make them leave 
the flues at no higher temperature than before. 

But the theoretical advantage of forced draught in respect 
of efficiency does not stop here. When the draught does not 
depend on the action of a chimney there is no need to let the 
escaping gases have any higher temperature than is imposed 
by the condition, already indicated, that they must be reasonably 
hotter than the temperature of the feed. With a chimney, on the 
other hand, as much heat is necessarily wasted as will keep the 
temperature of the escaping gases up to the comparatively high 
value necessary to maintain the draught. A chimney being an 
exceedingly inefficient form of heat-engine, the heat which is 
expended in maintaining its draught is vastly greater than the 
equivalent of the work that a fan would do in producing the same 
draught, or even than the heat that would have to be supplied to 
an engine employed in driving the fan. 


In practical instances in which the draught is forced, namely, 
in locomotives and in some marine and a few land engines, the 
theoretical advantages of forced draught, in respect of efficiency, 
are imperfectly realised. The draught has generally been forced 
with the object of increasing the power of a given boiler rather 
than of securing a high efficiency. The motive has been to bum 
more coal per square foot of grate surface, and to get a higher 
temperature in the furnace gases, so that more water may be 
evaporated in a boiler of given weight. This is incompatible with 
high efficiency, for to secure efficiency the heating surface must be 
largely increased that it may deal with the augmented total 
quantity and higher temperature of the furnace gasea It is clear 
however that the most efficient boiler would be one using a 
strong mechanically forced draught, with a relatively small area of 
grate and a relatively very large heating surface, extended by the 
use of a feed-water heater, so that not only the gases should 
be cooled as far as possible before escaping, but that the proportion 
of air to coal should be as small as is consistent with thorough 

204. Sources of loss of Heat. Ordinarily about seven- 
tenths and rarely more than eight-tenths of the potential energy of 
the fuel are conveyed to the steam. The remaining two or three- 
tenths are accounted for as follows: — (1) waste of fuel in the 
solid state by dropping through the grate ; (2) waste of fuel in the 
gaseous and smoky state by imperfect combustion; (3) waste of 
heat by external radiation and conduction ; and (4) waste of heat 
in the escaping gases due mainly to their high temperature, but 
partly also to their containing as one of the products of combustion 
a certain amount of steam-gas which passes off uncondensed. Of 
these sources of waste the first is generally trifling and the fourth 
is the most important If we assume the air of dilution to be 
12 lbs. the whole quantity of gas escaping from the chimney is 
25 lbs. per lb. of coal burnt. The specific heat of this gas is 
nearly that of air, say 0*24 thermal units (§ 36). Hence about 
6 thermal units are lost, per lb. of fuel burnt, for every degree by 
which the temperature of the escaping gas is allowed to exceed 
the lowest attainable limit. A chimney temperature of 600° Fah. 
is not unusual, and if we take 100° Fah. as a limit determined by 
the temperature of the feed- water, this represents a more or less 


preventable waste of 3000 thermal units, or in round numbers 
one-fifth of the whole energy of the coal. 

206. Chimney Draught. In a chimney draught the "head" 
(usually stated in inches of water pressure) under which the 
current of air is kept up is equal to the amount by which the 
weight of a column of air in the chimney falls short of the weight 
of a corresponding column of outside air. Except for their excess 
of temperature the contents of the chimney would be heavier than 
the air outside nearly in the ratio of n + 1 to n, where n is the 
number of pounds of air which have taken up 1 lb. of fuel in passing 
through the furnace. The actual density of the gases is less than 

T /ft "4" X\ 

that of the air outside in the proportion — ( j to 1 where 

T and To are the absolute temperatures inside and outside 
respectively. The diflference in actual density multiplied by the 
height of the chimney gives the eflfective head This head is used 
up partly in setting the column of air in motion and partly in 
overcoming the resistance to its passage which is offered by the flue, 
by the chimney itself, and by the grate. With a forced draught 
and a short chimney the resistance of the grate is the most import- 
ant of these items ; with a tall chimney on the other hand the 
resistance of the chimney itself comes to be so considerable that 
an increase of height produces almost no increase of draught, and 
may even diminish the draught if the sectional area is at all 
reduced in the added part. Under such conditions also there is a 
limit in the extent to which the draught will be assisted by 
letting the chimney temperature remain high. In raising the 
temperature of the chimney gases a stage is reached at which the 
gain in head and consequently in velocity of current is more than 
counterbalanced by the diminution of density, and if the gases are 
hotter than this the amount of gas passing through the chimney 
in a given time is actually reduced. In cases where the resistance 
is practically all met with after the gases have become heated — 
in other words, when the resistance of the grate is a very small 
part of the whole, the maximum draught is produced when the 
contents of the chimney have a density equal to half that of the air 
outside^ Assuming 24 lbs. of air to be admitted per lb. of fuel 
this condition is reached when the temperature in the chimney is 

^ See Rankine's Steam^Engine^ p. 289. 


about 600° Fah. or about the melting point of lead. When the 
resistance of the grate is a substantial part of the whole a rather 
higher temperature will make the draught a maximum. No 
advantage whatever is gained by making the temperature higher 
than corresponds to maximum draught, and on the score of thermal 
eflSciency a lower temperature is to be preferred, as diminishing 
the heat lost in the escaping gases. 

206. Boilers for Stationary Engines. Cornish and 
Lancashire Types. Most modem boilers are internally fired, 
that is to say, the furnaces are more or less completely enclosed 
within the boiler. Externally fired boilers are in general dis- 
tinctly less eflScient than internally fired boilers ; they are, how- 
ever, used to a considerable extent at coal-pits and other places 
where fuel is specially cheap or where the waste heat of other 
furnaces is to be utilized. Their usual form is that of a horizontal 
cylinder with convex ends ; the strength both of the main shell 
and the ends is derived from their curvature, and no staying is 
required. Generally the heating surface is entirely external and 
is of very limited extent. 

In large stationary boilers the forms known as the " Cornish " 
and "Lancashire'* are the most common. The shell of these 
boilers is a long horizontal cylinder with flat ends, and within this, 
stretching fi'om end to end within the water space, is a single 
large tube in the Cornish form and two parallel tubes in the 
Lancashire form, each tube containing a furnace at one end and 
communicating at the other end with external flues which are 
ai'ranged to make nearly all the external surface of the shell below 
the water line act as part of the heating surface. The remainder of 
the heating surface is given by the large tube or tubes which con- 
tain the furnace, with the addition generally of several short cross 
tubes containing water, which traverse the main furnace tube at 
right angles to its length and not only serve the purpose of en- 
larging the heating surface, but promote circulation in the water, and 
strengthen the main tube. Fig. 153 shows a Cornish boiler in lon- 
gitudinal section, and Fig. 154 is a cross section which shows the 
arrangement of the external flues. The furnace extends from the 
front up to the bridge of fire-brick C, In continuing their passage 
beyond this through the main tube or flue the hot gases come in 
contact with the cross-tubes, or Galloway tubes, DD, which have a 












2 S 

^ a 



Fig. 154. Transverse section of Cornish Boiler. 

Fig. 155. Transverse section of Lancashire Boiler. 




somewhat conical form that they may allow the steam formed in 
them to rise readily. At the end of the internal flue the gases are 
diverted downwards into the external flue B, and having traversed 
it towards the front of the boiler they are made to rise into the two 
side flues AA, by which they again pass to the back end and 
thence to the chimney. The form of the Lancashire boiler is 
essentially the same, except that there are two furnace tubes 
placed side by side, the diameter of the shell being larger. 
Fig. 155 is the cross-section of a Lancashire boiler. In a modified 
form of this boiler, introduced by Mr Galloway, the two furnace 
tubes unite beyond the bridge into one with a flat section, which 
is prevented from collapsing by having a number of Galloway 
tubes in it to act as stays. 

The shell of a Lancashire boiler is commonly about 28 feet 
long, with a diameter of 7 feet, which allows each of the two 
furnace tubes to be 2 feet 9 inches wide. A boiler of this size, 
burning 20 lbs. or so of coal per hour per square foot of grate, will 
evaporate about 6000 Iba of water per hour, or enough to yield, 
with an efficient condensing engine, from 300 to 400 indicated 

In boilers of this type the curvature of the cylindrical shell 
and furnace tubes enables them to resist the pressure of the 
steam : only the flat ends require to be stayed. This is done by 
means of gusset-stays EE (fig. 153), which tie the end plate to 
the circumference of the shell, and ofben also by means of longitu- 
dinal stay-bolts stretching from end to end within the water 
space. The furnace flues are made up of a series of short welded 
lengths united by joints which give the whole tube stiffness to 
resist collapse, but leave it some freedom to bend when the top 
expands more than the bottom through the unequal action of the 
fire. To provide for unequal expansion is one of the most 
important points in the design of a boiler : when it is neglected a 
racking action occurs which induces leakage at the joints and 
tends to tear the plates. For this reason the furnace flues are 
attached only to the end plates and not to the cylindrical part of 
the shell, and the stays of the end plates are arranged to leave these 
plates some freedom to bulge out and in when the flues lengthen 
and contract. 

^ For particulars of the Lancashire boiler see a paper by Mr L. E. Fletcher, 
Proc. Intt. Mech. Eng, 1876. 


207. Boiler Mountings. The steam dome, which used to 
be an ordinary feature in boilers of this type, is now generally 
omitted, and steam is taken direct from the steam space within 
the shell through a perforated " antipriming " pipe, from which it 
passes through a nozzle on the top of the boiler (fig. 153) to the 
stop-valve. The other openings on the top of the shell are 
the man-hole, on which a cover is bolted, and two openings for 
safety-valves. One of these valves is frequently of the dead- 
weight t3rpe, in which the force by which the valve is held closed 
is furnished by the direct action of a pile of weights : in many cases 
however springs and weighted levers are used. The second 
safety-valve is often arranged to form what is called a low-water 
safety-valve, being connected to a float in such a way that the 
valve will open if the water is allowed to sink below a safe level. 
At the bottom of the shell there is another nozzle for the blow-out 
cock, and in the front plate, below the furnace tubes there is 
another manhole. Feed water is supplied by a pipe which enters 
through the front plate on one side near the top of the water and 
extends a good way in, distributing the water by holes throughout 
its length. A pipe at the same level on the other side serves to 
collect scum. On the top of each frimace is a fusible plug (F, fig. 
153) which melts if the furnace crown become overheated. On the 
front plate are a pair of glass gauge tubes showing the level of the 
water within and a pressure gauge of the Bourdon type. This 
important fitting consists of a metal tube, oval in section, which is 
bent into a nearly circular form. One end is closed and is free to 
move : the other is held fixed and is open to the steam. The 
pressure of the steam tends to make the oval section rounder, and 
consequently tends, through ' anticlastic ' bending, to straighten 
the tube. The free end accordingly moves through a small 
distance which is proportional to the excess of pressure within 
the tube above the atmospheric pressure to which its outer surface 
is exposed, and this movement is magnified by an index turning 
on a dial. Most of the fittings which have been mentioned are 
common to boilers of all types. 

208. Mnltltubular Boilers. In several other forms of 
boiler an extensive heating surfiskce is obtained by the use of a 
large number of small tubes through which the hot gases pass. 
This construction is followed in locomotive and marine boilers, 




and boilers of the tjrpical locomotive and marine forms (to be 
presently described) are, especially the former, frequently used 
with stationary engines. The multitubular construction is also 
applied in some instances to boilers of the ordinary cylindrical 
form by making a host of small tubes take the place of that part 
of the flue or flues which lies behind the bridge, or by using small 
tubes as channels through which the gases return from the back 
to the front after they have passed through the main flue. Still 
another form of tubular boiler is an externally fired horizontal 
cylinder filled with return tubes extending from back to front. In 
all these forms the tubes are placed within the water space of the 
boiler. Except in locomotives the tubes are commonly of iron, 
and a usual diameter is about 3 inches. They give so much heating 
surface that the outside surface of the shell need not be used, and 
hence in a tubular boiler the external flues are dispensed with 
which are a necessary feature of the Cornish or Lancashire type. 

209. Vertical Boilers. In the boilers which have been 
referred to the axis of the cylindrical shell is horizontal. But the 
cylinder may be turned up on end and the boiler take a vertical 
form, the grate of course remaining horizontal and forming the 
floor of a fire-box to which access is given by a door on the side of 
the cylindrical shell. Large vertical boilers are now uncommon, but 
the type is a very usual one for boilers of small power. It has the 


Fig. 166. 

Fig. 167. 

Fio. 168. 


drawback that the free surface of the water from which the steam 
rises is comparatively small and consequently the steam rises 
with a higher velocity, which increases the risk of priming. 
Fig. 156 shows an ordinary small vertical boiler with Galloway 
tubes across the upper part of the fire-box; and Fig. 157 is 
another form, in which the water tubes are curved channels which 
allow the water to circulate from the space round the sides of the 
fire-box to the space above the crown. In other forms of vertical 
boiler the heating surface is increased by water tubes which hang 
from the crown of the fire-box and are closed at the lower end, 
circulation of water being maintained in them by means of a 
partition in the form of an inner tube inside of which water flows 
down to allow an upward movement of water and steam to be 
maintained between the inner tube and the outer. Tubes of this 
kind are called Field tubes, and are particularly used in the 
boilers of fire-engines and in other cases where steam has to 
be got up with the least possible delay. A section of a Field 
tube is given in fig. 158, with arrows to indicate the manner in 
which the water circulates. 

210. Watertube Boilers. Many forms of boiler have been 
designed in which the firing is external, and the heating surface is 
made up of the outer surface of numerous tubes or other small 
sectional parts, through which a circulation of water is kept up in 
virtue of the diflferences in density between the hotter and colder 
portions of the water. In ordinary boilers the circulation is more 
or less casual : when a bubble of steam is detached from any part 
of the heating surface its place is taken by water which may 
come in from any side. In a properly designed water-tube boiler 
the circulation is systematic : water enters each of the tubes at 
one end and passes through in a continuous thin stream, becoming 
partly converted into steam as it goes. The tubes generally 
deliver into a separating vessel, from the upper part of which the 
steam-pipe takes its supply, while water collects in the lower part 
to be returned by gravity to the lower end of the tubes. Boilers 
of this type can be constructed so as to have, with their contents, a 
relatively small total weight in proportion to the rate at which they 
can make steam, which is a distinct merit in respect of marine and 
especially naval use. For erection in some situations such as 
basement rooms they have the advantage that they can be 
brought together in small pieces. Further they are easily made 



strong enough to resist exceptionally high pressures owing to the 
absence of any large shell : an early tubular boiler, for instance, 
designed by Mr Lofbus Perkins delivered steam at 500 lbs. per 
square inch. 

A successful example of this type is the Babcock and Wilcox 
boiler (fig. 159), the heating surface of which is almost wholly 

Fig. 159. Baboook and Wilcox Boiler. 

composed of a series of inclined tubes up which water circulates 
in parallel streams. These are joined at their ends by cast-iron 
connecting boxes to one another and also to a horizontal drum on 
the top in which the mixture of steam and water which rises from 
the tube undergoes separation. At the lowest point of the boiler 
is another drum for the collection of sediment. The route taken 
by the hot gases is indicated by arrows in the figure. Root's boiler 
is another of very similar form. In the Belleville boiler the tubes 
are grouped in sets, each set forming a flattened helix through 
which the water rises ftx)m the sediment chamber to the separating 
drum. Harrison's boiler is a group of small globular vessels of 
cast-iron strung like beads on rods which tie them together. The 
Herreshof boiler is a continuous coil of tube, arranged as a 
dome over the fire. Feed water is pumped slowly through the 
coil, and turns to steam before it reaches the end. Here the 
circulation is mechanically forced instead of being due, as in the 
more usual forms, to diflferences of density in the contents. Another 
eflfective water-tube boiler (Niclausse's) is composed of a group of 



Field tubes arranged so that the inner tube, through which the 
water flows on its way to the heating surface opens out of one main 
drum or tube, while the outer member of each Field tube discharges 
steam and water into a second drum distinct from the first, but con- 
nected with it by a pipe through which the unevaporated water 
drains back. 

The construction of water-tube boilers has received much 
attention at the hands of Mr J. I. Thomycroft, especially in 
relation to marine engines. In his form of boiler* (fig. 160) the 

Mhw e^ ra^ 

Fio. 160. Thomyoroft Boiler. 
^ Min. Proe, Irut. C. E, Vol. xciz. p. 41. This paper also desoribes oiher forms 
and contains an important disoussion of the whole subject. See also papers on 
Water-tube Boilers read before the Institution of Nayal Architects, March, 1S94. 


entire heating surface is made up of tubes of an inch or an inch 
and a half in diameter and therefore not requiring to be more 
than one-tenth of an inch thick for the working pressure of 
200 or 250 lbs. The tubes form an arch over the fire and after 
bending out again terminate in the top of a separating drum 
from which the water drains by a pair of external pipes to the two 
drums which are seen at the base of the arch on either side. A 
boiler of this class fitted in a torpedo boat, with 1837 square feet 
of heating surface and 30 square feet of grate surface was tested 
by Professor Kennedy under various degrees of forced draught 
ranging up to a stoke-hole pressure of two inches of water*. 
Under the highest pressure of air it made enough steam to give 
775 indicated horse-power in the engine ; the heat used in making 
the steam was 67 per cent, of the whole energy of the fuel, 
and nearly 70 lbs. of coal were burnt per hour per square foot of 
grate. Analysis of the furnace gases showed that the supply of 
air per lb. of coal was 17*2 lbs., and that about 9 per cent, of the 
energy of the fuel was lost through imperfect combustion. In 
another trial when the air pressure in the stoke-hole was equivalent 
to only half-an-inch of water the engine gave 450 indicated horse- 
power, and with practically the same supply of air per lb. of coal 
78 per cent, of the energy was used in making steam and only 
5 per cent, was lost through imperfect combustion. These figures, 
and others which will be found in Professor Kennedy's report, 
show that a boiler of this kind can make steam with great 
freedom and with but little reduction in efficiency even when the 
draught is strongly forced, while its efficiency at more ordinary 
rates of output is remarkably high. Mr Yarrow's boiler is a some- 
what similar form, the chief difference being that its tubes are 
straighter and enter the separating drum below instead of above 
the water line. 

211. laOcomotiTe Boilers. The locomotive boiler consists of 
a nearly rectangular fire-box, enclosed above and on the sides by 
water, attached to a cylindrical part called the barrel, which extends 
horizontally from the fire-box to the front part of the locomotive 
and is filled with numerous horizontal tubes. Figs. 161 and 162 
show in Ipngitudinal and transverse section a boiler of the London 
and North- Western Bailway, which may be taken as typical of 
English practice. 

The barrel is 10 feet long and a little more than 4 feet in 
* Min. Proe. Irut. C, E. Vol. xcix. p. 57. 



diameter, and is made up of three rings of steel plates arranged 
telescopically. It contains 198 brass tubes, each IJ inches in 
external diameter. The front tube-plate in which the tubes 



terminate is of steel and is stayed to the back tube-plate by the 
tubes themselves, and the upper part of the front tube-plate 
above the tubes is also tied by longitudinal rods to the back end- 
plate. The fire-box is of copper and is nearly rectangular, with a 
horizontal grate. Bound its sides, front, and back (except where 
the fire-door interrupts) is a water space about 3 inches wide, 
which narrows slightly towards the bottom. The flat sides of the 
fire-box are tied to the flat sides of the shell by copper stay-bolts, 
4 inches apart, which are secured by screwing them into both 
plates and riveting over the ends. The crown of the fire-box is 
stiflfened by a number of girders on the top, to which the plates 
are secured by short bolts. The girders are themselves hung from 
the top of the shell above them by slings which are secured 
to angle-irons riveted on the inside of the shell plates. A sloping 
bridge of fire-brick partially separates the upper part of the fire- 
box from the lower and prevents the flame from striking the 
tubes too directly. Under the grate is an ashpan, to which the 
supply of air is controlled by a damper in front. The fire-door 
opens inwards, and can be set more or less open, to regulate the 
amount of air admitted above the fire. On top of the barrel is a 
steam-dome, from which the steam supply is taken through a pipe 
8 traversing the forward part of the steam space and passing 
down to the valve-chest through the smoke-box. The stop-valve 
or " regulator " R is situated in the smoke-box, and is worked by 
a rod through the boiler from the cab at the back. Above the 
fire-box end of the shell are a pair of Ramsbottom safety-valves, 
F, V — two valves pressed down by a single spring attached to the 
middle of a cross bar, which is prolonged to form a hand lever by 
which the valves may be eased up to see that they are free upon 
their seats. In front of the forward tube-plate is the smoke- 
box, containing a blast-pipe B by which the exhaust steam is 
used to produce a partial vacuum and so force a draught through 
the furnace. 

Instead of stiflfening the fire-box crown by the use of girder 
stays, the plan is sometimes followed of staying it directly to the 
shell above. The outer shell above the fire-box is generally 
cylindrical ; but to facilitate this method of stajdng it is some- 
times made flat. This construction is not unusual in American 
locomotive boilers, another feature of which is that the grate is 
made larger than in English practice, for the purpose of burning 


anthracite coal. An extreme instance is inmished by the Wooton 
engines of the Philadelphia and Reading Railroad, which bum 
small coal of poor quality in a fire-box 9 J feet long by 8 feet wide, 
extending over the trailing wheels of the engine. In some cases 
the fire-box is divided by a sloping partition of plates with water 
between, which crosses the fire-box diagonally from front to back 
and has in its centre an opening resembling a fire-door mouth- 
piece to allow the products of combustion to pass. In others the 
• fire-bridge is supported by water-tubes, and water-tubes are also 
used as grate-bars. This is done rather to promote circulation of 
the water than to give heating surface. The practice of American 
and English locomotive engineers diflfers somewhat as regards the 
materials of construction. American shells are of mild steel, 
English shells generally of mild steel but often of wrought-iron. 
In English practice the fire-boxes are of copper and the tubes of 
brass ; in America the fire-boxes are of mild steel and the tubes of 

The locomotive tjrpe of boiler is used for portable and semi- 
portable engines, and to a considerable extent for stationary 
engines of small and medium power. It also finds a place in 
marine practice in cases where lightness is of special advantage. 

212. Marine Boileni. So long as marine engines used 
steam of a pressure less than about 35 Iba per square inch the 
marine boiler was generally a box with flat sides, elaborately 
stayed, with a row of internal furnaces near the bottom opening 
into a spacious combustion-chamber enclosed within the boiler at 
the back, and a set of return tubes leading from the upper part of 
the chamber to the front of the boiler, where the products of 
combustion entered the uptake and passed off to the funnel. The 
use of higher pressures has made this form entirely obsolete. 
The normal marine boiler is now a short circular horizontal 
cylinder of steel, closed by flat plates at the ends, with internal 
furnaces in cyliudrical flues» internal combustion-chambers, and 
return tubes above the flues. In one variety, called the double- 
ended boiler, there are furnaces at both ends of the shell, each 
pair leading to a combustion-chamber in the centre that is 
common to both, or to separate central chambers with a water 
space between them. 

Figs. 163 and 164 show a double-ended marine boiler built 
by Messrs Gourlay Brothers for suppl}dng steam at a pressure 



of 165 lbs. to a triple-expansion en^e. At each end there 
are three furnaces in flues made of welded corrugated steel 
plates. The use of corrugated plates for flues, introduced by 


Mr Fox, makes thin flues able to resist collapse, and allows 
the flues to accommodate themselves easily to changes of tem- 
perature. One combustion-chamber is common to each pair of 
furnaces. It is strengthened on the top by girder stays and on 
the sides by stay-bolts to the neighbouring chamber and to the 
shell. The tubes are of iron, and a certain number of them are 
fitted with nuts so that they serve as stays between the tube-plate 
of the combustion-chamber and the front of the boiler. The 
upper part of the front plate is tied to the opposite end of the 
boiler by long stays. The uptakes from both ends converge to the 
funnel base above the centre of the boiler s length. The boiler 
shown is one of a pair, which lie side by side in the vessel, the 
uptake at each end being common to both. Each boiler in this 
example has a steam-dome, which is a part now often omitted, and 
from it the steam-pipe leads to the engine ; it consists of a small 
cylindrical vessel, with flat ends tied together by a central stay. 
Short pipes connect the dome near each end with the steam space 
of the main shell. The shell is 12J feet in diameter, and 16 J feet 
long. The plates are of mild steel 1^ inches thick round the shell 
and 1 inch in the ends, the corrugated flues are ^ inch thick. 
There are 127 tubes at each end, 46 of which are stay-tubes. 
The tubes are of iron, 3J inches in external diameter. Above 
these are 18 longitudinal steel stay-rods extending from one end- 
plate to the others in the steam space. The crowns of the 
combustion-chambers are stiflfened by girder stays and their sides 
and bottom by short stay-bolts which tie them to one another and 
to the shell. 

The single-ended marine boiler is practically half a double- 
ended boiler. The furnace doors are at one end only, and the 
boiler terminates in a flat end-plate which leaves only a few 
inches of water space between it and the back of the combustion- 
chambers, the end plate and the back plate of each chamber 
being tied together across this space by short stay-bolts. 

Reference has already been made to the use on board ship of 
boilers of the locomotive and water tube types as substitutes for 
these normal marine forms, the motive being to save weight, and 
also in some cases to use a higher pressure than can readily 
be borne by a large shell. It appears that before the steam 
pressure used in marine engines can undergo any increase at all 
comparable with that which occurred with the introduction of 



triple-expansion engines the present normal form of marine 
boilers must give place to one or other — ^probably the latter — of 
these two types. With the Thomycroffc boiler pressures as high 
as 250 lbs. per square inch have been used, but generally with triple- 
expansion engines only, the object having been to minimise the 
weight of the plant rather than to secure the highest efficiency. 
To do justice to this pressure would require quadruple expansion. 

213. Feeding boilers. The Injector. Boilers are usually 
fed either by a feed-pump driven by the engine, or by a distinct 
auxiliary engine called a "donkey," or by an injector. The 
injector, invented by the late M. Giffard, and now very generally 
used on locomotive a^d other boilers, is illustrated in fig. 165. 
Steam enters from the boiler at A and blows through an annular 
orifice B, the size of which is regulated by the handle C. The 
feed- water flows in at D, and meeting the steam at B causes it to 

Sitam ^rmrn Hffffiiator 

Fig. 166.--Giffard*8 Injector. 


condense. This produces a vacuum at B, and consequently the 
water rushes in with great velocity, and streams down through 
the combining nozzle /, its velocity being augmented by the 
impact of steam on the back of the column. In the lower part of 
the nozzle E the stream expands ; it therefore loses velocity, and, 
by a well-known hydrodjuamic principle, gains pressure, until at 
the bottom its pressure is so great that it enters the boiler 
through a check- valve which opens only in the direction of the 
stream. The orifice F which is in communication with the narrow 
end of the combining nozzle I and leads to the overflow pipe Q 
allows the injector to start into action, by providing a channel 
through which steam and water may escape until the stream 
acquires enough energy to force its way into the boiler. The 
opening for admitting water between D and B is regulated by the 
wheel H, The form of injector shown in the sketch is substantially 
the original form introduced by Giffard : variations in it have been 
made by many makers. In some of these the injector is classified 
as non-lifting, that is to say it requires the supply of water to 
come from a source at a level not lower than that of the injector. 
The non-lifting injector requires fewer adjustable parts : the steam- 
regulating cone B is omitted. The exhaust-steam injector works 
by steam from the exhaust of non-condensing engines, instead of 
using live steam from the boiler. The steam orifice is then larger 
in proportion to the other parts, the volume of the steam supply 
being greater. In self-starting injectors an arrangement is pro- 
vided by which overflow will take place freely until the injector 
starts into action and then the openings are automatically adjusted 
to suit delivery into the boiler. One plan of doing this is to make 
the combining nozzle under the steam orifice in a piece which is 
free to slide in the outer casing. Until the injector starts it lies at 
some distance from the steam orifice, and allows free overflow ; but 
when the vacuum forms it rises, in consequence of pressure at the 
base. In self-adjusting injectors this rise of the combining nozzle 
is made use of to contract the water-way round the steam orifice. 
In another form of self-starting injector one side of the combining 
nozzle is in the form of a hinged flap, which opens backwards to allow 
overflow to take place, but closes up when a vacuum is formed and 
the injector starts into action^ Weir's hydroldneter for large marine 

^ See papers in Proe. Imt. Mech. Eng, 1860, 1866, 1884. For the theoxy of the 
injeetor, see Peabody's ThennodynamicM of the Steam-Engine^ Chapter x. 


boilers is another apparatus in which the principle of the injector 
is made use of, with the object of promoting circulation of the 
water during the time steam is being raised It consists of a 
series of nozzles, with water-inlets between them, through which 
water is drawn by means of a central jet of steam supplied from a 
donkey boiler. The ejector-condenser of Mr Morton is another 
apparatus in which the principle of the injector is applied. 

214. Feed-water heaters. In the boilers of factory and 
other stationary engines the use of a feed- water heater to extract 
from the furnace gases more heat than the heating surface of the 
boiler will itself take up, is common even when (as is generally 
the case) the chimney is relied on to maintain the draught. 
Green's "economizer*' is a well-known form, in which the water 
passes through tubes the outer surface of which is exposed to the 
hot gases and kept clear of deposited soot by the continuous action 
of a mechanical scraper. A precisely similar construction has been 
made to serve as a superheater, and the two have been used together, 
the hot gases coming first into contact with the tubes of the super- 
heater and then, at a slightly lower temperature, with those of 
the feed-water heater. In locomotives and other non-condensing 
engines a portion of the exhaust steam is frequently made use of 
to heat the feed-water. When an exhaust-steam injector is 
employed it serves the purpose of a feed-water heater as well as 
that of a feed-pump. Besides increasing the efficiency of the 
boiler by utilizing what would otherwise be waste heat, a feed- 
water heater has the advantage that by raising the temperature 
of the water it removes air, and also, in the case of hard water, 
causes lime and other substances held in solution to be deposited 
in the heater instead of being carried into the boiler, where they 
would form scale. In Weir's feed-heater for marine engines the 
temperature of the feed-water is raised to about 200° Fahr. by 
injecting steam from the intermediate receiver. When a donkey 
pump is used for feeding boilers the feed is often heated by 
allowing the steam used by the donkey to be condensed in it. 

216. Use of Zinc to prevent corrosion in boilers. To 

prevent corrosion in boilers it is usual to introduce blocks of zinc 
in metallic connexion with the shell. These are set in the water 
space, preferably at places where corrosion has been found specially 
liable to occur. Their function is to set up a galvanic action, 


in which zinc plays the part of the negative element, and is 
dissolved while the metal of the shell is kept electro-positive. 
Otherwise there would be a tendency for diflferences of electric 
quality between different parts of the shell to set up galvanic 
actions between the parts themselves, by which some parts, being 
negative to others, would be attacked. The zinc raises the 
potential of the whole shell enough to make all parts positive 
relatively to the water. 

216. Methods of forcing draught. The simplest but by 
no means the most economical way of forcing the draught is to let 
a jet of steam from the boiler discharge itself up the chimney. It 
tends to carry the furnace gases with it and so to reduce the air 
pressure in the surrounding space. Allusion has already been 
made to the system which is universal in locomotive boilers of 
utilizing the exhaust steam from the engine as a means of forcing 
the draught. Two methods of mechanically forcing the draught 
have come into extensive use in marine practice. One plan is to 
box in the stokehole and keep the air in it at a pressure of from 1 
to 3 inches of water by the use of blowing fans. In Mr Howden's 
system of forced draught the stokehole is open, and air is 
supplied by a blowing fan to a reservoir formed by enclosing 
the ashpit and also to another reservoir from which air gets 
access to the grate above and through the fire-door. On its 
way to the reservoir the air is heated by passing across a part of 
the uptake in which the hot gases from the furnace are led through 
tubes. This method of restoring to the ftimace what would other- 
wise be waste heat forms an interesting alternative to the method 
of restoring heat to the boiler by passing the hot gases through a 
feed- water heater ; it is in fact an application to boiler furnaces of 
the regenerative principle alluded to in Chap. 11.^ 

By either of these means the power of the boiler is increased 
in the ratio of 3 to 2, or even more, as compared with its power 
under chimney draught. The eflSciency of the boiler is, in general, 
slightly but not very materially reduced. Arrangements are often 
made which allow the chimney draught to serve in ordinary 
steaming and the fan to be resorted to when an exceptional 
demand for power has to be met : in other cases the pressure at 

^ A description and disonsuon of these altematiye methods of forcing draught 
will be found in papers read before the Institution of Naval Architects, April 1886. 

K . 21 


which air is supplied and consequently the rate of combustion 
of fuel on the grate is regulated by varying the speed of the 
fan. The facility which forced draught offers for adapting a boiler 
to a wide range of power has been illustrated in the experiments 
quoted in § 210. An ordinary marine boiler bums 15 to 20 lbs. 
of coal per hour per square foot of grate with natural draught, and 
this is easily raised to 30 lbs. or more under forced draught. A 
locomotive using the steam blast will bum 70 or 80 lbs. per 
hour per square foot of grate, and in boilers of the locomotive 
type which have been employed in torpedo boats a consumption 
at the rate of 140 lbs. has been reached. In such cases however 
the efficiency is low, for the combustion is not very perfect 
and the temperature of the escaping gases is high. 

217.. Mechanical Stoking. Many appliances have been 
devised for the mechanical supply of coal to boiler furnaces, but 
these have hitherto taken the place of hand-firing to only a very 
limited extent. In Juckes's furnace the fire-bars are in short 
lengths, jointed by pins to form a continuous chain or web, which 
rests on rollers and is caused to travel slowly in the direction of 
the furnace's length by pin-wheels round which the web is carried 
at the fi-ont and back. Coal is allowed to drop continually on the 
travelling grate fi-om a hopper in front of the furnace. A more 
usual form of mechanical stoker is a reciprocating shovel or ram 
which is supplied with coal fix>m a coal-hopper, and throws or 
pushes a small quantity of coal into the fire at each stroke. 
Along with this devices are employed for making the grate self- 
cleansing, by giving alternate fire-bars a rocking or sliding motion 
through a limited range. In Mr Crampton's dust-fuel furnace the 
coal was ground to powder and fed by rollers into a pipe from 
which it was blown into the furnace by an air-blast. This gave so 
intimate a mixture of fuel and air that the excess of air required 
for dilution was only one-fifth of the amount required for com- 
bustion\ A similar advantage attends the use of gaseous -fuel, and 
of liquid fuel that is blown into the furnace in the form of spray. 

218. Liquid Fuel. The use of liquid fuel for boilers has of 
late acquired importance, mainly in connexion with the discovery 
of petroleum, in large quantity, at Baku on the Caspian Sea. 

1 Proc. Inst. Mech. Eng, 1869. 


The heavy petroleum refuse which is left after distilling paraffin 
from the crude oil forms an exceedingly cheap fuel, with a calorific 
value about one-third greater than that of an equal weight of 
coal. It has superseded coal in the steamers of the Caspian, and 
has been very largely employed for locomotives in the south- 
eastern part of Russia. The oil is injected in the form of spray 
near the foot of the fire-box by a steam jet which is arranged 
in such a way that air is drawn into the furnace along with 
the petroleum. In the arrangements for burning petroleum 
introduced in Russian locomotives by Mr T. Urquhart the flame 
impinges on a structure of fire-brick, built in the fire-box with 
numerous openings to allow the gases to diffuse themselves 
throughout the combustion-chamber. This guards against a too 
intense play of flame on the metallic surfaces, and at the same 
time the bricks serve as a reservoir of heat to rekindle the 
flame should the combustion be intermittent In getting up 
steam an auxiliary boiler is used to supply the jet which serves 
to convert the oil into spray and to inject it along with air into 
the furnace^ Owing to the cost and danger of transporting 
oil in bulk its use as furnace fiiel, although perfectly successful 
in the neighbourhood of the oil wells, has hitherto been almost 
wholly restricted to certain districts. In England however Mr 
Holden has used with some success the residuum fi-om shale- 
oil distilleries with tar and other heavy liquid refuse as a 
substitute for coal in locomotives of the Great Eastern Bailway. 
Obvious advantages of liquid fuel are the ease with which the 
rate of combustion can be regulated to suit sudden changes 
in the demand for steam, also the nicety with which the supply 
of air taken in by the oil injector can be adjusted, and the 
continuity with which the fuel is supplied, its entrance requiring 
no opening of the fire-door with a consequent inrush of cold air. 

1 Urquhart, Min. Proc, Itut. C. E. 1884. 




219. Terms used In clwriflcHtloiL In classifying engines 
with regard to their general arrangement of parts and mode of 
working, account has to be taken of a considerable number of 
independent characteristic& We have, first, a general division 
into candenging and non-condensing engines^ with a subdivision of 
the condensing class into those which act hj surfisu^ condensation 
and those which use injection. Next there is the division into 
compound and non-^>ompoundy with a further classification of the 
former as double-, triple-, or quadruple-expansion engines. Again, 
engines may be classed as single or douUe-^bcting, according as the 
steam acts on one or alternately on both sides of the piston. 
Again, a few engines — such as steam-hammers and certain kinds 
of steam-pumps — are non-rotative, that is to say, the reciprocating 
motion of the piston does work simply on a reciprocating piece ; 
but generally an engine does work on a continuously revolving 
shaft, and is termed rotative. In most cases the crank-pin of the 
revolving shaft is connected directly with the piston-rod by a 
connecting-rod, and the engine is then said to be direct-acting ; in 
other cases, of which the ordinary beam-engine is the most 
important example, a lever is interposed between the piston and 
the connecting-rod. The same distinction applies to non-rotative 
pumping engines, in some of which the piston acts directly on the 
pump-rod, while in others it acts through a beam. The position 
of the cylinder is another element of classification, giving horizontal, 
vertical, and inclined cylinder engines. Many vertical engines are 
further distinguished as belonging to the inverted cylinder class; 
that is to say, the cylinder is above the connecting-rod and crank. 


In osdllabing cylinder engines the connecting-rod is dispensed 
with; the piston-rod works on the crank-pin, and the cylinder 
oscillates on trunnions to allow the piston-rod to follow the 
crank-pin round its circular path. In trunk engines the piston-rod 
is dispensed with ; the connecting-rod extends as far as the piston, 
to which it is jointed, and a trunk or tubular extension of the 
piston, through the cylinder cover, gives room for the rod to 
oscillate. In rotary engines there is no piston in the ordinary 
sense ; the steam does work on a revolving piece, and the necessity 
is thus avoided of afterwards converting reciprocating into rotary 
motion. Steam turbines may be said to form an extreme develop- 
ment of this rotary class. Still another mode of classification 
speaks of engines in reference to the conditions under which they 
are to work, as stationary, locomotive, or marine. 

220. Beam-Engines. In the single-acting atmospheric 
engine of Newcomen the beam was a necessary feature ; the use of 
water-packing for the piston required that the piston should move 
down in the working stroke, and a beam was needed to let the 
counterpoise pull the piston up. Watt's improvements made the 
beam no longer necessary ; and in one of the forms he designed it 
was discarded — ^namely, in the form of puraping-engine known as 
the Bull engine, in which a vertical inverted cylinder stands over 
and acts directly on the pump-rod. But the beam type was 
generally retained by Watt, and for many years it remained a 
favourite with the builders of large engines. The beam formed a 
convenient driver for pump-rods and valve-rods ; and the parallel 
motion which had been invented by Watt as a means of guiding 
the piston-rod could easily be applied to a beam-engine, and was, 
in the early days of engine-building, an easier thing to construct 
than the plane surfaces which are the natural guides of the 
piston-rod in a direct-acting engine. In modern practice the 
direct-acting type has almost wholly displaced the beam type. 
For mill-driving and the general purposes of a rotative engine 
the beam tjrpe is now rarely chosen. In pumping engines it is 
more common, but even there the tendency is to use direct-acting 

The only distinctive feature of beam-engines requiring special 
notice here is the "parallel motion,'* an ordinary form of which is 
shown diagrammatically in fig. 166. There MN is the path in which 


the piston-rod head, or crosshead, as it is often called, is to be guided. 
ABC is the middle line of half the beam, C being the fixed centre 
about which the beam oscillates. A link BD connects a point in 

s my 

Fia. 166.— Watt's ParaUel Motion. 

the beam with a radius link ED, which oscillates about a fixed 
centre at E. A point P in BD, taken so that BP:DP::EN: CM, 
moves in a path which coincides very closely with the straight line 
MPN. A.nj other point F in the line CP or CP produced is made 
to copy this motion by means of the links AF and FO, parallel to 
BD and AC, In the ordinary application of the parallel motion a 
point such as -P is the point of attachment of the piston-rod, and 
P is used to drive a pump-rod. Other points in the line CP 
produced are occasionally made use of, by adding other pairs 
of links parallel to -4(7 and BD. 

Watt's linkage gives no more than an approximation to 
straight-line motion, but in a well-designed example the amount 
of deviation need not exceed one four-thousandth of the length of 
the stroke. It was for long believed that the production of an 
exact straight-line motion by pure linkage was impossible, until 
the problem was solved by the invention of the Peaucellier cell. 
The Peaucellier linkage has not been applied to the steam- 
engine, except in isolated cases. 

In by far the greater number of modem steam-engines the 
crosshead is guided by sliding on planed surfaces. In many beam- 
engines, even, this plan of guiding the head of the piston-rod has 
taken the place of the parallel motion. 

221. Direct-acting Horizontal and Vertical Engines. 

This plan of guiding the piston-rod head is practically uni- 
versal in engines of the direct-acting class: the piston, the 
connecting-rod and the crank constitute a " slider-crank-chain " 
with the frame or bed-plate of the engine to form the fourth 


No type of steam-engine is so common as the horizontal 
direct-acting. In small forms the engine is generally self-contained, 
in other words a single frame or bed-plate carries all the parts 
including the main bearings in which the crank-shaft with its fly- 
wheel turns. The cylinder either rests on the bed-plate, or 
overhangs at the back, being in the latter case bolted to a vertical 
part of the frame which forms a cover for the front end of the 
cylinder. The frame is often given what is called a girder shape, 
which brings a portion of it more directly into the line of thrust 
between the cylinder and the crank centre, and allows the upper 
as well as the lower of the two surfaces which serve as guides for 
the crosshead to be formed on the frame itself. This construction 
is found in many small engines and is also usual in large engines 
of the Corliss type. The feed-pump plunger is usually driven 
from a separate excentric : in some cases it is directly attached to 
the crosshead, and in others to the valve-rod. When a condenser 
is used with a small horizontal engine it is usually placed behind 
the cylinder, and the air-pump, which is within the condenser, is 
a horizontal plunger or piston-pump worked by a 'tail-rod' — that 
is, a continuation of the piston-rod past the piston and through 
the back cover of the cylinder. In large horizontal engines the 
condenser generally stands in a well between the cylinder and 
the crank-shaft, and the pump, which has a vertical stroke, is 
worked by means of a bell-crank lever attached by a link to the 
crosshead of the engine. 

When uniformity of driving effort or the absence of dead- 
points is specially important, two independent cylinders often 
work on the same shaft by cranks at right angles to each other, 
an arrangement which allows the engine to be started readily 
from any position. Such engines are called coupled. The ordinary 
locomotive is an example of this form. Winding engines for mines 
and collieries, in which ease of starting, stopping, and reversing is 
essential, are very generally made by coupling a pair of horizontal 
cylinders, with cranks at right angles to each other, on opposite 
sides of the winding-drum, with the link-motion as the means of 
operating the valves. 

Direct-acting engines of the larger class are generally com- 
pounded either (1) by having a high and a low pressure cylinder 
side by side, working on two cranks at exactly or nearly right 
angles to each other, or (2) by placing one cylinder behind the 


other, with the axes of both in the same straight line. The 
latter is called the tandem arrangement. In it one piston-rod 
is generally common to both cylinders ; occasionally, however, the 
piston-rods are distinct, and are connected to one another by 
a framing of parallel bars outside of the cylinders. Another con- 
struction, rarely followed, is to have parallel cylinders with both 
piston-rods acting on one crank by being joined to opposite ends 
of one loDg, crosshead. In a few compound engines the large 
cylinder is horizontal, and the other lies above it. in an inclined 
position, with its connecting-rod working on the same crank- 

In tandem engines, since the pistons move together, there is 
no need to provide a receiver between the cylinders. It is practic- 
able to follow the " Woolf" plan (§ 140) of allowiog the steam to 
expand directly from the small into the large cylinder ; and in many 
instances this is done. In any case, however, the connecting-pipe 
and steam-chest form an intermediate receiver of considerable 
size, which will cause loss by " drop" (§ 42) unless steam be cut 
off in the large cylinder before the end of the stroke. Hence it 
is more usual to work with a moderately early cut-off in the 
low-pressure cylinder than to admit steam to it throughout the 
whole stroke. Unless it is desired to make the cut-off occur 
before half-stroke, an ordinary slide-valve will serve to distribute 
steam to the large cylinder. For an earlier cut-off than this a 
separate expansion-valve is required on the low-pressure cylinder, 
to supplement the slide-valve ; and in any case, by providing a 
separate expansion-valve, the point of cut-off is made subject to 
easy control, and may be adjusted so as to avoid drop or to divide 
the work as may be desired between the two cylinders. For this 
reason it is not unusual to find an expansion-valve, as well as 
a common slide-valve, on the low-pressure cylinder even in tandem 
engines. In many cases, however, the common slide-valve only 
is used. In the high-pressure cylinder of compound engines, 
the cut-off is usually effected either by an expansion slide-valve 
or by some form of Corliss or other trip-gear. 

For mill engines the compound tandem and compound coupled 
types are the most usual, and the high-pressure cylinder is very 
generally fitted with Corliss gear. In the compound coupled 
arrangement the cylinders are on separate bed-plates, and the 
fly-wheel is between the cranks. The use of triple expansion 


engines in mill-driving is extending but is still comparatively 

The general arrangement of vertical engines differs little from 
that of horizontal engines. The cylinder is usually supported 
above the shaft by a cast-iron frame resembling an inverted A, 
whose sides are kept parallel for a part of their length to serve as 
guides for the crosshead. Sometimes one side of the frame only 
is used, and the engine is stiffened by one or more wrought-iron 
columns between the cylinder and the base on the other side. 
Wall-engines are a vertical form with a flat frame or bed-plate, 
which is fixed by being bolted against a wall ; in these the shaft 
is generally at the top. Vertical engines are compounded, like 
horizontal engines, either by coupling parallel cylinders to cranks 
at right angles (or at 120° if triple expansion is to be used, as in 
the ordinary marine form) or, tandem fashion, by placing the high- 
pressure cylinder above the other. In vertical condensing engines 
the condenser is situated near the base under the back limbs of 
the frame, and the air-pump, which has a vertical stroke, is 
generally worked by a horizontal lever connected by a short link 
to the crosshead. In some cases the pump is horizontal, and is 
worked by a crank on the main shafts 

222. Single-acting high speed Engines. The ordinary 
double-acting engine, whether of the horizontal or vertical variety, 
may be adapted to a high speed by lightening its reciprocating 
parts, enlarging its bearing surfaces, and taking pains to secure 
symmetry and balance in the design. Mr Thomycroft, for example, 
has reached a speed of 1000 revolutions per minute in the engines 
built by him to drive fans for forcing the draught of torpedo boats. 
And even the comparatively large engines of a thousand horse- 
power or more which drive the propellers in these vessels are made 
to run at 400 or 500 revolutions per minute, mainly through the 
use of exceptionally large bearing surfaces. Several successful 
instances of the double-acting high speed might be named, but 
the high speed engines most usually met with are of the single- 
acting type. Steam is admitted to the back of the piston only, 
and the connecting-rod is in compression throughout the whole 

^ For particulars of the usual forms taken by engiues, see Haeder's Handbook of 
the Steam-Engine, Tran. by H. H. P. Powles (1893). The oonetruotion of details 
is discussed in Unwinds Elements of Machine Design, Vol. ii. 



revolution. Besides simplifying the valves, this has the important 
advantage that alternation of strain at the joints may he entirely 
avoided, with the knocking and wear of the brasses which it is apt 
to cause. To secure, however, that the connecting-rod shall 
always push, there must be much cushioning during the back or 
exhaust stroke, for reasons which have been explained in Chapter 
X. From a point near the middle of the back stroke to the 
end the piston is being retarded ; cushioning must begin at that 
point or earlier, and the work spent upon the cushion must at 
every stage be at least as great as the loss of energy on the 
part of the piston and rods. In some single-acting engines this 
cushioning is done by compressing a portion of the exhaust 
steam; in others the rod is kept in compression by help of a 
supplementary piston, on which steam from the boiler presses ; in 
the Willans engine the cushioning is done by compressing air. 
The demand for an engine which should run fast enough to drive 
a djuamo directly, without a belt or other intermediate gearing 
to multiply the speed, has done much to bring engines of this 
class into use. 

An early example is the three-cylinder engine introduced by 
Mr Brotherhood in 1873, a recent form of which is shown in 
figs. 167 and 168. Fig. 167 is a longitudinal and fig. 168 a trans- 
verse section. Three cylinders, set at 120° apart, project from a 

Fio. 167.— Brotherhood's Three-Cylinder Engine: longitudinal section. 

closed casing, the central portion of which communicates with 
the exhaust. The pistons have the trunk form — that is to say, 



there is a joint in the piston itself which allows the piston-rod to 
oscillate, and so makes a separate connecting-rod unnecessary. 
The three rods work on a single crank-pin, and the balance weights 
are on a pair of crank cheeks on the other side of the shaft. 
Steam is admitted to the back of the pistons only. It passes 
first through a throttle-valve, which is controlled by a centri- 
fugal spring-governor (fig. 167), and is then distributed to the 
cylinders by three piston-valves worked by an eccentric, the 
sheave of which is made hollow so as to overhang one of the 
main bearings. Release takes place by the piston itself uncover- 
ing exhaust ports in the circumference of the cylinder, and the 
rocking motion of the piston-rod is taken advantage of to open a 
supplementary exhaust port (fig. 168), which remains open during 
a sufficient portion of the back stroke. The flexible coupling 

Fia. 168,— Brotherhood's Three-Cylinder Engine: transverse section. 

shown at the right-hand end of the shaft in fig. 167, transmits 
the twisting moment of the shaft through disks of leather, and 
so prevents straining of the shaft and bearings through any want 
of alignment between the shaft of the engine and that of the 
mechanism it drives. Besides its use as a steam-engine, Mr 
Brotherhood's pattern has been extensively applied in driving 
torpedoes by means of compressed air. As a steam-engine it is 
compounded by placing a high-pressure cylinder outside of and 
tandem with each of the three low-pressure cylinders. 

In other single-acting engines the cylinders are placed side by 
side above the shaft, to act on two or on three cranks. The cranks 
and connecting-rods are completely enclosed, and are lubricated by 


dipping into a mixture of oil and water with which the lower part 
of the casing' is filled. In the Westinghouse engine, where there 
are two vertical cylinders to which steam is admitted by piston- 
valves, and the crank-shafb is situated half a crank's length out of 
the line of stroke, to reduce the effect of the connecting-rod's 
obliquity during the working stroke. 

To this type also belongs the Willans " central valve " engine 
which has been repeatedly referred to in Chapter V. in con- 
nection with the late Mr Willans* important experimental work. 
The exceptional efficiency of this engine in regard to consumption 
of steam, together with the facility it gives for driving a dynamo 
direct, and the small bulk which is a consequence of the high 
speed, has led to its being extensively used at electric lighting 
stations and elsewhere, in sizes ranging up to about 500 horse- 
power. In the compound and triple forms the successive 
cylinders are set tandem, in a vertical line, and the space below 
the upper piston serves as* intermediate receiver. In some 
cases a single crank is used, but generally two or three sets of 
cylinders are grouped in parallel lines above a corresponding 
number of cranks. The piston-rod of each set of cylinders is 
hollow, and has a piston-valve in it, worked by an eccentric on the 
crank-pin, and arranged so that the relative movement of this 
valve with respect to the hollow rod determines the admission, 
transfer, and exhaust of the steam. The cross-head is itself a 
piston, working in a hollow cylindrical guide, which becomes 
closed during the up-stroke so that air may be compressed in it to 
serve as a cushion and prevent the stress at the crank-pin from 
ever changing from push to pull. The work stored in this 
air-cushion during the up-stroke is restored during the down- 
stroke, almost without loss. The eccentric rod which works the 
valve is also as a rule kept in compression by the pressure of the 
live steam on the topmost piston-valve. The rod is split up into 
two parallel parts and the valve eccentric is set between them, its 
sheave being forged on the crank -pin so that the relative motion of 
the valve to the piston-rod which encloses it may be the same as the 
motion which a valve in an ordinary engine performs relatively to 
its fixed seat when the valve is moved by an eccentric on its 
shaft. These features will be better understood by reference to 
fig. 169, which gives a section through the two lines of cylinders in 
a two-crank compound engine. The two lines are alike, but the 



drawing shews the piston-rod in section on the left-hand side, in 
order to let the piston-valves inside it be seen. Steam enters 

Fio. 169. Willans' Central Valve Engine. 

the steam-chest at the top through a double beat throttle-valve A, 
which is controlled by a centrifugal governor. It is admitted to 
the topmost cylinder through the ports B and C in the hollow 


piston-rod or "trunk." Cut*off occars when the ports B are 
covered by disappearing into the gland of the top cylinder 
cover as the piston-rod descends. Subsequently, the relative 
motion of the valve rod within makes the valve F^ cover the port 
Cy and (near the end of the down-stroke) puts the ports C and D in 
communication with each other between the valves F, and Fi, in 
order to allow the steam which has expanded in the first or upper 
cylinder to pass into the space between the upper piston and the 
cover of the second cylinder below. During the back-stroke the 
steam passes into this space, which serves as intermediate receiver, 
and thence is admitted, in the next down-stroke, into the second 
cylinder in just the same way as it was admitted into the first. 
For triple expansion a third cylinder is placed below the second, 
and the steam passes through it in the same way during a third 
revolution of the engine. It finally escapes to the exhaust chamber, 
the position of which is marked on the figure. The part of the 
stroke at which cut-off occurs is regulated by adjusting the height 
of the glands in the top of each cylinder cover. The air buffer is 
contained in the guide cylinders EE, 

223. Pumping Engines. In engines for pumping water 
and other liquids, or for blowing air, it is not essential to drive a 
revolving shaft, and in many forms the reciprocating motion of 
the steam-piston is applied directly or through a beam to produce 
the reciprocating motion of the pump-piston or plunger without 
the intervention of any revolving part. On the other hand^ 
pumping and blowing engines are frequently made rotative for 
the sake of adding a fly-wheel. When the level of the suction 
water is sufficiently high, horizontal engines, with the pump 
behind the cylinder and in line with it are generally preferred ; 
in other cases a beam-engine or vertical direct-acting engine is 
more common. Horizontal engines are, however, employed to 
pump water from any depth by using triangular rocking frames, 
which serve as bell-crank levers between the horizontal piston 
and vertical pump-rods. For deep-well or mine pumping the 
Cornish type still finds employment with its single cylinder, 
single action, and cataract control. The non-rotative engine 
frequently takes a double-acting and compound form, as for 
instance in fig. 170 which shews a compound inverted vertical 
primping engine of this class, by Messrs Hathom, Davey and Co. 
Steam is distributed through lift valves, and the engine is 


governed by the differential gear illustrated in fig. 136, in conjunc- 
tion with a cataract, which makes the pistons pause at the end of 
each stroke. The pistons are in line with two pump-rods, and are 
coupled by an inverted beam which gives guidance to the cross- 
heads by means of a link-work which produces an approximate 
straight-line motion. 

Fio. 170. Vertical Non-Rotative Pumping Engine. 

Engines of this kind, like the old Cornish pump, are able to 
work expansively in consequence of the great inertia of the 
reciprocating pieces, the chief of which are the long and massive 
pump-rods. Notwithstanding the comparatively low frequency of 
the stroke, enough energy is stored in the movement of the rods 
to counterbalance the inequality with which the expanding steam 
works in different portions of the stroke, and the rate of accelera- 
tion of the system adjusts itself to give, at the plunger end, the 
nearly uniform effort which Ls required in the pump. In other 
words, the motion (instead of being almost simply harmonic as it 
is in a rotative engine) is such that the form of the inertia curve, 
when drawn as in fig. 141, is nearly the same as that of the steam 
curve, with the result that the distance between the two, which 
represents the effective effort on the pump-plunger, is nearly 
constant. The massive pump-rods may be said to form a re- 
ciprocating fly-wheel. 

It is however only to deep-well pumping that this applies, and 


a very numerous class of direct-acting non-rotative steam-pumps 
have too little mass in their reciprocating parts to allow such 
an adjustment to take place at any ordinary speed. A feimiliar 
example is the small donkey pump used for feeding boilers, which 
has its steam-piston and pump-plunger on the same piston-rod. 
In such engines an auxiliary rotative element is often introduced, 
partly to secure uniformity of motion and partly for convenience 
in working the valves; a connecting rod, for instance, is sometimes 
taken from a point in the piston-rod to a crank shaft which 
carries a fly-wheel, or a slotted cross-head is fixed to the rod 
and gives motion of rotation to a crank-pin which gears in the 
slot, the line of the slot being perpendicular to that of the 
stroke. But many pumps of this class are purely non-rotative, 
and in such cases the steam is generally admitted throughout 
the whole of the stroke, since the inertia of the parts is not 
suflBcient to give the means of reconciling uniformity . of pump- 
eflfort with expansive working. In some of these the valve is 
worked by tappets from the piston-rod. In the Blake steam- 
pump a tappet worked by the piston as it reaches each end of 
its stroke throws over an auxiliary steam-valve, which admits 
steam to one or other side of an auxiliary piston carrying the 
main slide-valve. In Cameron and Floyd's form one of a pair of 
tappet- valves at the ends of the cylinder is opened by the piston 
as it reaches the end of the stroke, and puts one or other side 
of an auxiliary piston, which carries the slide-valve, into com- 
munication with the exhaust, so that it is thrown over. Often 
the working of the valve is secured by using a " duplex " pair of 
cylinders, and arranging them so that the motion of one controls 
the valve of the other. In the Worthington steam-pump, for 
example, two steam-cylinders are placed side by side, each working 
its own pump-piston. The piston-rod of each is connected by a 
short link to a swinging bar, which actuates the slide-valve of the 
other steam-cylinder. In this way one piston begins its stroke 
when the motion of the other is about to cease, and a smooth 
and continuous action is secured^ 

The Worthington engine has been extensively applied, 
on a large scale, to raise water for the supply of towns and to 
force oil through "pipe-lines" in the United States. In the 
larger sizes it is made compound, each high-pressure cylinder 

^ For particulars of the performanoe of several small pumping engines of this 
dass see Proc. Inst. Mech, Eng. Oct. 1893. 


having a low-pressure cylinder tandem with it on the same rod. 
To allow of expansive working, an ingenious, device is added 
which compensates for the inequality of effort on the pump-piston 
that would result from an early cut-off. A cross-head A (fig. 171) 
fixed to each of the piston-rods is connected to the plungers of 
a pair of oscillating cylinders B, B, which contain water and 
communicate with a reservoir full of air compressed to a pressure 
of about 300 lb. per square inch. When the stroke (which takes 
place in the direction of the arrow) begins these plungers are at first 
forced in, and hence work is at first done by the main piston-rod, 
through the compensating cylinders B, B, 
on the compressed air in the reservoir. 
This continues until the crosshead has 
advanced so that the oscillating cylinders 
stand at right angles to the line of stroke. 
Then for .the remainder of the stroke 
their plungers assist in driving the 
main piston, and the compressed air gives 
out the energy which it stored in the 
earlier portion. The volume of the air reservoir is so 
greater than the volume of the cylinders B, B that the 
sure in it remains nearly constant throughout the stroke, 
leakage from the cylinders or reservoir is made good by a small 
pump which the engine drives. One advantage which this 
method of equalizing the effort of a steam-engine piston has (as 
compared with making use of the inertia of the reciprocating 
masses) is that the effort, when adjusted to be uniform at one 
speed, remains nearly uniform although the speed be changed, 
provided the inertia of the reciprocating parts be small. In the 
Worthington "high-duty" engine, where this plan is in use, the 
high and low-pressure cylinders are each provided with a separate 
expansion-valve of the rocking-cylinder type, as well as a slide- 
valve ; the cut-off is early, and the efficiency is as high as in other 
pumping-engines of the best class. The results obtained in tests 
of these engines have been referred to in Chapter V. 

Another method of compensating for the inequality of the 
piston thrust during expansion in non-rotative pumping-engines 
is to connect the pistons not directly but through a rocking piece 
in such a way that the steam-piston gets a mechanical advantage 
over the pump-piston as the stroke proceeds. This has been done 
E. 22 



by Mr Davey in cases where the reciprocating pieces have not 
enough inertia to make a compensating device unnecessary. A 
roddng sector between the pistons causes their velocity ratio, 
which is nearly one of equality in the early portion of the stroke, 
to alter as the stroke goes on, with the result that in the later 
stages as the steam pressure falls off the pump-piston moves more 
slowly than the steam-piston. 

224. The puliometer. Mr Hall's '"pulsometer" is a peculiar 
pumping-engine without cylinder or piston, which may be regarded 
as the modem representative of the engine of Savery (§ 6). The 
sectional view, fig. 172, shows its principal parts. There are two 
chambers A, A\ narrowing towards the top, 
where the steam-pipe B enters. A ball-valve 
G allows steam to pass into one of the chambers 
and closes the other. Steam entering (say) 
the right-hand chamber forces water out of it 
past the clack-valve F into a delivery passage 
D, which is connected with an air-vessel. 
When the water-level in A sinks so far that 
steam begins to blow through the delivery- 
passage, the water and steam are disturbed 
and so brought into intimate contact, the 
steam in A is condensed, and a partial vacuum 
is formed. This causes the ball-valve G to 
rock over and close the top of A , while water 
rises from the suction-pipe E to fill that 
chamber. At the same time steam begins to enter the other 
chamber A\ discharging water from it, and the same series of 
actions is repeated in either chamber alternately. While the 
water is being driven out there is comparatively little condensation 
of steam, partly because the shape of the vessel does not promote 
the formation of eddies, and partly because there is a cushion of 
air between the steam and the water. Near the top of each 
chamber is a small air-valve opening inwards, which allows a little 
air to enter each time a vacuum is formed. When any steam is 
condensed, the air mixed with it remains on the cold surface and 
forms a non-conducting layer. Further, when the surface of the 
water has become hot the heat travels very slowly downwards so 
long as the surface remains undisturbed. The pulsometer of course 
cannot claim high efiiciency as a thermodynamic engine, but its 

Fig. 172. Pulsometer. 



suitability for situations where other steam-pumps cannot be used* 
and the extreme simplicity of its working parts, make it valuable 
in certain cases. Trials of its performance have shown that under 
favourable conditions a pulsometer may use no more than 160 lbs. 
of steam per effective horse-power-hour. This consumption does not 
compare unfavourably with that of small non-rotative steam-pumps^ 

226. Davey's safety motor. We have seen that the ten- 
dency of modem steam practice is towards high pressures, and 
that this means a gain both in efficiency 
and in power for a given weight of 
engine. High pressure, or indeed any 
pressure materially above that of the 
atmosphere, is out of the question 
when engine and boiler are to work 
without the regular presence of an 
attendant. Mr Davey has introduced 
a small domestic motor which deserves 
notice from the fact that it employs 
steam at atmospheric pressure. One 
form of this engine is shown in fig. 173. 
The boiler — which serves as the frame 
of the engine — is of cast-iron in the 
example shown in the drawing, though 
in more recent cases a steel boiler has 
been substituted. It is fitted with a 
cast-iron internal fire-box, with a vertical flue which is traversed 
by a water-bridge. The cylinder, which is enclosed within the 
upper part of the boiler, and the piston are of gun-metal, and 
work without lubrication. Steam is admitted by an ordinary 
slide-valve, also of gun-metal, worked by an eccentric in the usual 
way. The condenser stands behind the boiler; it consists of a 
number of upright tubes in a box, through which a current of cold 
water circulates from a supply-pipe at the bottom to an overflow- 
pipe at the top. In larger sizes of the motor the cylinder stands 
on a distinct frame, and the boiler has a hopper fire-box, which 
will take a charge of coke sufficient to drive the engine for several 
hours without attention. About 6 or 7 lb. of coke are burned per 

1 Proe, Inst. Mech, Eng, 1893, p. 456. An automatic yalve is described in the 
same place which enables the pulsometer to use steam expansively. 


Fig. 173. Davey motor. 


226. Rotary Engines. From the earliest days of the 
rotative engine attempts have been made to avoid the intermittent 
reciprocating motion which an ordinary piston-engine first produces 
and then converts into motion of rotation. The design of rotary 
engines, to use the name generally applied to non-reciprocating 
forms, haj3 exercised the ingenuity of many inventors, with results 
which in general have little value or interest except to the student 
of applied kinematics. Murdoch, the contemporary of Watt, 
proposed an engine consisting of a pcdr of spur-wheels g^earing 
with one another in a chamber through which steam passed by 
being carried round the outer sides of the wheels in the spaces 
between successive teethe 

In a more modem wheel-engine (Dudgeon's) the steam was 
admitted by ports in side-plates into the clearance space behind 
teeth in gear with one another, just after they had passed the line 
of centres. From that point to the end of the arc of contact the 
clearance space increased in volume; and it was therefore possible, 
by stopping the admission of steam at an intermediate point, to 
work expansively. The difficulty of maintaining steam-tight 
connexion between the teeth and the side-plates on which the 
faces of the wheels slide is obvious; and the same difficulty 
has prevented the success of other forms of rotary engine. 
These have been devised in immense variety, in many cases, it 
would seem, with the idea that a distinct mechanical advantage 
was to be secured by avoiding the reciprocating motion of a 
piston'. In point of fact, however, very few forms entirely escape 
having pieces with reciprocating motion. In all rotary engines, 
with the exception of steam turbines, — where work is done by the 
kinetic impulse of steam, — there are steam chambers which 
alternately expand and contract in volume, and this action usually 
takes place through a more or less veiled reciprocation of working 
parta So long as engines work at a moderate speed there is little 
advantage in avoiding reciprocation ; the alternate starting and 
stopping of piston and piston-rod does not aflfect materially the 
Motional efficiency, throws no deleterious strain on the joints, and 
need not disturb the equilibrium of the machine as a whole. The 
case is diflferent when very high speeds are concerned ; it is then 

^ See Farey's Trtatut on the Steam-Engine, p. 676. 

3 A large number of proposed rotary engines are described, and their kinematic 
relations to one another are discussed, in Beuleauz*s Kinematics of Mackinen/t 
translated by Prof. Kennedy. 


desirable as far as possible to limit the amount of reciprocating 
motion and to reduce the masses that partake in it. 

A comparatively recent example of the rotary type in which 
reciprocating motion occurs only to a trifling extent is the 
spherical engine of Mr Beauchamp Tower^ This engine was, like 
several of its predecessors', based on the kinematic relations of the 
moving pieces in a Hooke's joint. Imagine a Hooke's joint, con- 
necting two shafts set obliquely to one another, to be made up of 
a central disk to which the two shafts are hinged by semicircular 
plates, each plate working in a hinge which forms a diameter of the 
central disk, the two hinges being on opposite sides of the disk and 
at right angles to one another. Further, let the disk and the 
hinged pieces be enclosed in a spherical chamber through whose 
walls the shafts project. As the shafts revolve each of the four 
spaces bounded by the disk, a hinged piece, and the chamber wall 
will suflfer a periodic increase and diminution of volume, between 
limits which depend on the angle at which the shafts are set. In 
Mr Tower's engine this arrangement is modified by using spherical 
sectors, each nearly a quarter sphere, in place of semicircular plates, 
for the hinged pieces in which the shafts terminate. The shafts are 
set at 136° to each other. Each of the four enclosed cavities then 
alters in volume from zero to a quarter sphere, back to zero, again to 
a quarter sphere, and again back to zero, in a complete revolution 
of the shafta In practice the central disk is a plate of finite thick- 
ness, whose edge is kept steam-tight in the enclosing chamber by 
spring-packing, and the sectors are reduced to an extent corre- 
sponding to the thickness of the central disk. One shaft is a 
dummy and runs free, the other is the driving-shaft. Steam is 
admitted and exhausted by ports in the spherical sectors, whose 
backs serve as revolving slide-valves. It is admitted to each 
cavity during the first part of each periodical increase of the 
cavity's volume. It is then cut oflf and allowed to expand as the 
cavity further enlarges, and is exhausted as the cavity contracts. 
If the working shaft, to which the driven mechanism serves as a 
fly-wheel, revolves uniformly, the dummy shaft is alternately 
accelerated and retarded. Apart from this, the only reciprocating 
motion is the small amount of oscillation which the comparatively 
light central disk undergoes. 

1 Proc. Inst, Mech. Eng.^ March 1885. 

^ One of these, the disk-engine of Bishop, was used for a time in the printing- 
office of The Times, but was discarded in 1857. 


Another rotary engine of the Hooke's-joint family is Mr 
Fielding's, in which a gimbal-ring and four curved pistons take the 
place of the disk. Two curved pistons are fixed on each side of 
the gimbal-ring, and as the shafts revolve these work in a corre- 
sponding pair of cavities, which may be called curved cylinders, 
fixed to each shaft. 

227. Steam Turbinei. A strictly rotary or non-reciprocating 
type of engine is found in the steam turbine, where rotation of 
a wheel is produced either by impact of a jet upon revolving 
blades, or by reaction firom a jet of escaping steam, as in the 
seolipile of Hero (§ 2). In order that a revolving piece should 
extract, either by impulse or reaction, a respectable fraction of 
the kinetic energy of a steam jet, it must move with immense 
velocity. Mr C. A. Parsons, who has brought the steam turbine to 
so remarkable a level of efficiency that its performance rivals that 
of the best piston and cylinder engines, has overcome this difficulty 
by making the action compound, in other words, he uses a series 
consisting of several sets of turbine wheels arranged so that the steam 
acts on each in succession. After leaving the first set of turbine 
blades the steam passes through a set of fixed guide blades which 
direct it against the next set of moving blades, and so on, with the 
result that although only a small part of its energy is taken up by 
each set, the amount taken up by the whole series is large, and a 
high efficiency is secured without giving the turbine blades an 
excessive velocity. A single shaft carries all the turbines. In 
the original form of the Parsons turbine the wheels were of the 
central flow type: in a later form the steam flows radially 
outwards through a series of rings of blades fixed on one face 
of each wheel. Between each ring and the next is a ring of 
fixed blades held in position on the face of an annular disc which 
projects inwards from the circumference of the case in which the 
turbines are enclosed. After struggling through the series of 
rings of blades on the first wheel, the steam passes inwards over 
the back of that wheel to the central region of the next wheel, 
where again it struggles outwards through alternate rings of 
revolving turbine blades and fixed guide-blades. The action 
is repeated on wheel after wheel until the pressure of the steam is 
reduced to the value at which release is to occur, which may be as 
low as a good air-pump will produce in a condenser. The turbine 
is therefore able to work like a condensing steam-engine, and does 



in fact realise the economic advantage of high expansion. In an 
example tested by the writer, when the output was at a rate 
approaching 150 eflfective horse-power, the steam was expanded 
from an absolute pressure of 115 lbs. per square inch to 1 lb. 
per square inch, and the amount of steam which was used per 
horse-power hour was not more than it would have been in 
a first-class compound engine. 

Fig. 174 shows a portion of this turbine in cross-section, 
A1A2A2 are three of the revolving wheels or discs which carry the 


M^ jk 



Fio. 174. Section of part of Parsons' Steam Turbine. 

turbine blades. BijBjS, are the corresponding fixed rings which 
carry the guide-blades. The guide-blades project towards the 
right from the fixed rings J5, the turbine blades towards the left 
from the moving discs A, and fixed and moving blades alike are 
of such a height that there is very little clearance between their 
ends and the opposing disc or ring. Steam enters the turbine 
through a double-beat valve and first reaches the innermost ring of 


blades between Ai and JBi. Having acted on the successive rings 
of blades carried by Ai it returns towards the centre between the 
backs of Ai and B^, to act in turn on the blades of A^, then on 
As and so on. In this example there were six discs A, each 15 inches 
in diameter, and a seventh, the diameter of which was 26f inches, 
and the whole number of rings of turbine blades was 35. The blades 
are of sheet brass, slightly curved, and set so that the apertures 
between them are wider the further the steam has expanded. The 
one-sided character of the discs would produce an end-thrust on 
the turbine shaft, but this is balanced by a revolving baffle-piston 
C, which has a number of deep grooves on its circumference which 
are entered by corresponding annular projections on a fixed bush 
resembling the thrust-block of a marine propeller shaft. The high 
speed of the shaft (4800 revolutions per minute in this instance) 
requires special forms of bearing and special means of lubrication 
to be adopted. The main bearings stand in a bath of oil, which is 
kept in constant circulation by means of a pump, and the bushes in 
which the shaft turns consist of several concentric sleeves fitting 
loosely over one another so that a film of oil may find its way 
between each sleeve and the one outside it. This leaves the shaft 
some little freedom to adjust itself by lateral displacement, but at 
the same time the viscosity of the oil films acts as a powerful 
damper to prevent oscillations from being set up. One of these 
main bearings is contained in the oil-case D on the left of the 
figure. The speed is controlled by making the admission of steam 
take place not continuously, but in gusts at regular intervals, the 
duration of each gust being automatically regulated (by means of 
a steam relay governor) to suit the demand for work. The gusts 
are produced by the periodic lifting and dropping of the double beat 
valve shown in the figure. When the engine is working under its 
full load the gusts become blended into an almost continuous blast 
In the tests referred to above the turbine was used to drive a 
dynamo, the armature shaft of which was directly coupled to the 
turbine shaft. Trials were made at various grades of output, 
ranging up to 137 electrical horse-power, the quantity of steam 
used per hour being determined in relation to the electrical horse- 
power developed by the djniamo. The steam was superheated to a 
moderate extent by passing through pipes in the boiler flue. The 
air-pump of the condenser was driven by a separate engine, whose 
consumption of steam is not included in the measurements. 



The following table gives some of the results, which are also 
shown in fig. 175, by means of curves drawn in the manner 

ao 60 TO 80 90 lOO 110 

Eleetrieal Horse-Power 
Fio. 175. Besults of Steam Turbine Trials. 

Table XII. Trials of SteamrTurbine Dynamo with steam 
superheated ahout 60° F. 

I20 ISO 140 

Feed water per hoar in lbs. 

Boiler presanre 
by gauge 

of steam. 

Oot-put in 

lbs. per aq. in. 





Per electrical 
































explained in § 139. It will be seen from this figure that the 
** Willans line" for the steam turbine is very nearly straight, and 
that the rate of out-put may be reduced to one-half the fall load, 
or less, with .no more than a small increase in the consumption of 
steam. If we take the net electrical out-put to represent say 75 
per cent, of the work done by the steam — ^a proportion which 
would roughly hold good in ordinary cases — the performance of 
the turbine dynamo is equivalent at full load to that of an engine 
consuming less than 16 lbs. of steam per indicated horse-power- 
hour. With so moderately high a steam-pressure as 100 lbs. this 
performance rivals the best examples quoted in Chapter V. The 
600 lbs. or so of steam used per hour when the net electrical 
horse-power is zero is the quantity required to keep the turbine 
shaft running at its normal speed and to maintain the electrical 
out-put of the "exciting" dynamo, which is not included in the 
figures as part of the net electrical power. 

In De Laval's steam turbine the steam passes through a 
diverging nozzle forming a single jet which impinges against 
the turbine blades, with an action resembling that of the water 
in a Pelton wheel. The velocity of the blades is 500 feet per 
second or more. The jet escapes at the pressure of the atmosphere, 
and the whole expansion is performed in a single step. 

228. Marine Engines. The early steamers were fitted with 
paddle-wheels, and the engines used to drive them were for the 
most part modified beam-engines. Bell's " Comet" (§ 21) was 
driven by a species of inverted beam-engine, and another form 
of inverted beam, known as the side-lever engine, was for long a 
favourite with marine engineers. In the side-lever engine the 
cylinder was vertical, and the piston-rod projected through the 
top. From a crosshead on the rod a pair of links, one on each side 
of the cylinder, led down to the ends of a pair of horizontal beams 
or levers below, which oscillated about a fixed gudgeon at or near 
the middle of their length. The two levers were joined at their 
other ends by a crosstail, firom which a connecting-rod was taken 
to the crank above. The side-lever engine is now obsolete. In 
American practice, engines of the beam type, with a braced-beam 
supported on A frames above the deck, are still found in river- 
steamers and coasters. 

An old form of direct-acting paddle-engine was the steeple- 


engine, in which the cylinder was set vertically below the crank. 
Two piston-rods projected through the top of the cylinder, one on 
each side of the shaft and of the crank. They were united by 
a crosshead sliding in vertical guides, and from this a return- 
connecting-rod led to the crank. 

Modem paddle-wheel engines are usually of one of the 
following kinds. (1) In oscillating cylinder engines the cylinders 
are set under the crank-shaft, and the piston-rods are directly 
connected to the cranks. The cylinders are supported on trunnions 
which give them the necessary freedom of oscillation to follow the 
movement of the crank. Steam is admitted through the trunnions 
to slide-valves on the sides of the cylinders. In some instances 
the mean position of the cylinders is inclined instead of vertical ; 
and oscillating engines have been arranged with one cylinder 
before and another behind the shaft, both pistons working on one 
crank. The oscillating cylinder tjrpe is best adapted for what 
would now be considered comparatively low pressures of steam. 
(2) Diagonal engines are direct-acting engines of the ordinary 
connecting-rod type, with the cylinders fixed on an inclined bed 
and the guides sloping up towards the shaft. 

When the screw-propeller began to take the place of paddle- 
wheels in ocean-steamers, the increased speed which it required 
was at first supplied by using spur-wheel gearing in conjunction 
with one of the forms of engines then usual in paddle steamers. 
After a time types of engine better suited to the screw were 
introduced, and were driven fast enough to be connected directly 
to the screw-shaffc. The smallness of the horizontal space on 
either side of the shaft formed an obstacle to the use of horizontal 
engines, but this difficulty was overcome in several ways. In 
Penn's trunk-engine, which was at one time a usual form in war 
vessels the engine was shortened by attaching the connecting-rod 
directly to the piston, and using a hollow piston-rod, called a 
trunk, large enough to allow the connecting-rod to oscillate inside 
it. The trunk extended through both ends of the cylinder and 
formed a guide for the piston. The trunk engine had the draw- 
back of requiring very large stuffing-boxes, of wasting cylinder 
space, and of presenting a large surface of metal to alternate 
heating by steam and cooling by contact with the atmosphere. 

The return-connecting-rod engine is another horizontal form 
which was used in the navy. It is a steeple-engine placed horizon- 


tally, with two, and in some cases four, piston-rods in each cylinder. 
The piston-rods pass clear of the shaft and the crank, and are 
joined beyond it in a guided crosshead, from which a connecting- 
rod returns. 

Ordinary horizontal direct-acting engines with a short stroke 
and a short connecting-rod are also found in war-ships, where the 
horizontal was at one time generally preferred to the vertical type 
of engine for the sake of keeping the machinery below the 
water-line. In horizontal marine engines the air-pump and 
condenser are placed on the opposite side of the shaft from 
the cylinder, which balances the weight and allows the air-pump 
to be driven direct. 

In merchant ocean-steamers one general type of engine is 
universal, and the same type is now to an increasing extent 
adopted in naval practice. This is the inverted vertical direct- 
acting engine. Its most usual form has three cylinders set in line 
fore and aft above the shaft, working on cranks at 120'' from 
one another, and emplojdng triple expansion. The mechanical 
advantage of three cranks in giving a nearly uniform turning 
moment with but little resultant thrust against the shaft has had 
much to do with the general adoption of this form. A slide-valve 
serves, without any separate expansion valve, to control the 
distribution of steam in each cylinder, the cut-oflF being capable of 
variation by " notching up" the link-motion or other reversing gear 
through which the slide-valve is operated. In most instances the 
cylinders are without steam-jackets. 

Surface condensation was introduced in marine practice by 
S. Hall in 1831, but was not brought into general use until much 
later. Previous to this it had been necessary, in order to avoid 
the accumulation of too dense brine in the boiler, to blow off 
a portion of the brine at short intervals and replace it by sea- 
water, a process which of course involved much waste of heat. By 
the use of surface condensers it became possible to use the same 
portion of water over and over again. The very freedom of the 
condensed water from dissolved mineral substances was for a time 
an obstacle to the adoption of surface condensers, for it was found 
that the boiler, no longer protected by a deposit of scale, became 
rapidly corroded through the action of acids formed by the 
decomposition of the lubricating oil This objection was overcome 
by introducing a sufficient amount of salt water to allow some 


scale to form, and the use of surface condensers soon became 
universal on steamers pljdng in sea-water. The marine condenser 
consists of a multitude of tubes, generally of brass, about | of an inch 
in diameter. Through these cold sea- water is made to circulate, 
while the steam is brought into contact with their outside surfaces. 
In some cases, especially in Admiralty practice, cold water 
circulates outside the tubes and the steam passes inside. 

The ordinary marine engine has four pumps: — the air-pump, 
which is made large enough to serve in case injection instead of 
surface-condensation should at any time be resorted to ; the feed- 
pump ; the circulating-pump, which maintains a current of sea- water 
through the tubes of the condenser; and the bilge-pump, which 
discharges any water that may gather by leakage or otherwise 
in the bilge of the ship. The pumps are so arranged that in the 
event of a serious leak the circulating-pump can also draw its 
supply from the bilge. In many engines, especially those of less 
recent construction, the four pumps are placed behind the con- 
denser, and are worked by a single crosshead driven by a lever, the 
other end of which is connected by a short link with one of the 
crossheads of the engine. It is now usual to have a small engine, 
distinct from the main engine, to drive the feed-pump, and to 
supply circulating water by a centrifugal or other pump also driven 
by a separate engine. 

229. Relation of power to weight in Marine Engines. 

In the improvement of the marine engine two points have been 
particularly aimed at, — ^reduction in the rate of consumption of 
coal per horse-power, and reduction in the weight of the machine 
(comprising the engine proper and the boilers) per horse-power. 
The second consideration is in some cases of even more moment 
than the first, especially in war-ships. Progress has been made, in 
both respects, by increase of steam-pressure, and, in the second 
respect especially, by increase of piston speed. The gain in 
economy which came with rise in boiler pressure has been referred 
to in § 21. As to the reduction in weight, Messrs Marshall and 
Weighton, in a paper dealing with this subject ^ have pointed out 
that before the introduction of triple expansion and forced draught 
the weight of engines in the mercantile marine, including the 

^ IfarshaU and Weighton, Proe, North-Eatt Coast Intt, Engineers and Ship- 
huilders, 18S6. 


boilers and the water in them, was 480 lb. per i.-a-P. In the 
navy this was reduced, chiefly by the use of lighter framing with 
the object of minimizing weight, to 360 lb. Triple engines of the 
merchant tjrpe, without forced draught, are only slightly lighter 
than double engines ; but in naval practice, where forced draught, 
greatly increased speed, and the use of steel for firames and working 
parts have combined to reduce the ratio of weight to power, a 
marked reduction in weight is apparent. To quote examples, a set 
of vertical triple engines, which indicate 2200 H.-P. with natural 
draught, and 4000 H.-P. with a draught forced by pressure in 
the stokehole equal to 2 inches of water, weigh under the latter 
condition (along with the boilers) only 155 lb. per I.-H.-P. In 
another set, in which the draught is forced by a pressure of 3 
inches, and the cylinders are only 15^, 24 and 37 inches in 
diameter, with a stroke of 16 inches, the indicated horse-power is 
4200, and the weight of engines and boilers is 136 lb. per I.-H.-P. 
In these the boilers are of the locomotive type, and the mean 
piston speed is 1066 feet per minute. Even these light weights 
are surpassed in smaller engines, such as those of torpedo-boats. 
In so far as this immense developement of power from a small 
weight of machinery is due to high piston speed, it is secured 
without loss — indeed with some gain — of thermodynamic eflSiciency ; 
forced draught, however, without a corresponding extension of the 
heating surface, leads to a less efficient expenditure of fuel. With 
a given type of engine there is a certain ratio of expansion which 
gives a minimum in the ratio of weight to power ; when this ratio 
of expansion is exceeded the engines have to be enlarged to an 
extent that more than counterbalances the saving in boiler weight ; 
when a less ratio of expansion is used the boilers have to be 
enlarged to an extent that more than counterbalances the reduc- 
tion of weight in the engine proper^ 

230. Iiocomotives. The ordinary locomotive consists of a 
pair of direct-acting horizontal or nearly horizontal engines, fixed 
in a rigid frame under the front end of a boiler of the type 
described in § 211, and coupled to the same shaft by cranks at 

^ On the general subject of marine engines, referenoe should be made to 
Mr A. E. Seaton*s Manual of Marine Engineering ; to Mr B. Bennett's Treatise 
on the Marine Steam-Engine; and to Mr W. H. Maw's Recent Practice in 
Marine Engineering, 


right angles, each with a single slide-valve worked by a link- 
motion, or by a form of radial gear. The engine is non-condensing, 
except in special cases, and the exhaust steam, delivered at the 
base of the fiinnel through a blast-pipe, serves to produce a 
draught of air through the fomace. In some instances a portion 
of the exhaust steam, amounting to about one-fifth of the whole, is 
diverted to heat the feed-water. In tank engines the feed-water 
is carried in tanks on the engine itself; in other engines it is 
carried behind in a tender. 

On the shaft are a pair of driving-wheels, whose frictional 
adhesion to the rails furnishes the necessary tractive force. In 
some engines there is a single pair of driving-wheels ; in many 
more a greater tractive force is secured by having two equal 
driving-wheels on each side, connected by a coupling-rod between 
pins on the outside of the wheels. In goods engines a still greater 
proportion of the whole weight is utilized to give tractive force by 
coupling three and even four wheels on each side. These arrange- 
ments are distinguished by the terms "four-coupled," '* six-coupled," 
and "eight-coupled" applied to the engines. In inside-cylinder 
engines the cylinders are placed side by side within the frame of 
the engine, and their connecting-rods work on cranks in the 
driving shaft. In outstde-cylinder engines the cylinders are spread 
apart far enough to lie outside the frame of the engine, and to 
work on crank-pins on the outsides of the driving-wheels. This 
dispenses with the cranked axle, which is apt to be the weakest 
part of a locomotive engine. Owing to the frequent alternations of 
strain to which it is subject, a locomotive crank-axle is peculiarly 
liable to rupture, and has to be removed after a certain amount of 

In some locomotives the leading wheels are coupled to driving- 
wheels behind them, but it is now generally preferred to have 
under the front of the engine two or four smaller wheels which da 
not form part of the driving system. These are carried in a bogie, 
that is, a small truck upon which the front end of the fiume rests 
by a swivel-pin or plate which allows the bogie to turn, so as to 
adapt itself to curves in the line, and thus obviate the grinding of 
tyres and danger of derailment which would be caused by using a 
long rigid wheel-base. The bogie appears to have been of English 
origin* ; it was brought into general use in America, and is now 

1 Min. Proc, Inst, C. JS., vol. liii. p. 60. 


common in English as well as in American practice. Instead of a 
four-wheeled bogie, a single pair of leading wheels are also used, 
carried by a Bissel pony truck, which has a swing-bolster pivoted 
by a radius bar about a point some distance behind the axis of the 
wheels. This has the advantage of combining lateral with radial 
movement of the wheels, both being required if the wheel base is 
to be properly accommodated to the curve. Another method of 
getting lateml and radial freedoni is the plan used by Mr Webb of 
carrjdng the leading axle in a box curved to the arc of a circle, 
and free to slide laterally for a short distance, under the control of 
springs, in curved guides*. 

In inside-cylinder engines the slide-valves are frequently 
placed back to back in a single valve-chest between the cylinders. 
The width of the engine within the frame leaves little room for 
them there, and they are reduced to the flattest possible form, in 
some cases with split ports, half above and half below a partition 
in a central horizontal plane. In a few engines the valves are 
below the cylinders, with feces sloping down towards the front, 
while the cylinders themselves slope slightly up. In many more 
the valves work on horizontal planes above the cylinders; this 
position is specially suitable when Joy's or some other form of 
radial gear is used instead of the link-motion. Radial valve-gears 
have the advantage, which is of considerable moment in inside- 
cylinder engines, that the part of the crank-shaft's length which 
would otherwise be needed for eccentrics is available to increase 
the width of main bearings and crank-pins, and to strengthen the 
crank-cheeks. Walshaert's gear is very extensively used on Con- 
tinental locomotives, and Joy's has been applied to a large number 
of British engines. 

The outside-cylinder type is adopted by several British makers; 
in America it is universal. There the two castings which form 
the cylinders are bolted together to make a saddle on which the 
bottom of the smoke-box sits. The slide-valves are on the tops of 
the cylinders, and are worked through rocking levers from an 
ordinary link-motion. 

231. Compound Iiocomotives. Locomotive engines have 
been compounded in several ways ; but it is still an open question 
whether compound working oflfers any distinct advantage, when 

1 Proe, Inst. MeeK Eng., 18S3. 


regard is had to convenience in driving and cost of repairs as well 
as to economy in fuel 

In 1876 Mr A. Mallet introduced, on the Bayonne and Biarritz 
Railway, a type of compound locomotive in which one small 
high-pressure cylinder and one large low-pressure cylinder were 
used in place of the two equal cylinders of a common locomotive. 
Outside cylinders were used in the first instance, but Mallet's 
system is also applied to inside-cylinder engines. The pipe from 
the high to the low-pressure cylinder takes a winding course 
through the smoke-box ; this gives it a sufficient capacity to serve 
as intermediate receiver, and also dries the steam before it enters 
the large cylinder. A reducing valve is provided through which 
steam of a pressure lower than that of the boiler can be admitted 
direct to the low-pressure cylinder to facilitate starting. The 
reversing gear is arranged to act on both cylinders by one 
movement, and also to permit a separate adjustment of the cut-off 
in each. Engines on Mallet's system have been successfully used 
on other Continental railways and in India, in some instances by 
conversion from the non-compound form. His plan has the 
advantage of permitting this conversion to be made (in cprtain 
cases), and of requiring scarcely any more working parts than 
are needed in a common locomotive; but it gives an unsym- 
metrical engine. He has also proposed an engine with four 
cylinders, — one high-pressure cylinder tandem with one low- 
pressure cylinder on each side. Another symmetrical form has 
been used, in which a pair of outside high-pressure cylinders 
are compounded with a pair of inside low-pressure cylinders. 
In England, on the North-Eastem Railway, Mr T. W. Worsdell 
has made extensive use of compound engines, employing two 
cylinders only which stand side by side inside the frame with 
valves on the top worked by Joy's gear. 

The most important experiment yet made in this direction 
is that which Mr F. W. Webb, of the London and North- 
Western Railway, has been conducting on a large scale since 
1881. In Mr Webb's system three cylinders are used. Two 
equal high-pressure cylinders are fixed outside the frames, and 
drive the rear driving axle by crank-pins set at right angles to one 
another. A single low-pressure cylinder of very large size is placed 
beneath the smoke-box, and drives a crank in the middle of the 
forward driving axle. The driving axles are not coupled, and the 
£. 23 


phase-relation of the low-pressure to the high-pressure stroke is 
liable to alter through unequal slip on the part of the wheels. 
This, however, is of no material consequence, on account oY the 
large size of the intermediate receiver and the uniformity with 
which the two high-pressure cylinders deliver steam to it. The 
receiver is formed, as in Mr. Mallet's arrangement, by leading long 
connecting pipes through the smoke-box. All three slide-valves 
are worked by Joy's gear. Those of the low-pressure cylinders 
are placed below the cylinders (an arrangement which has the 
advantage of letting the valve fall away from the port-fiw^ when 
the engine is running down-hill with the steam- valve closed); 
the valve of the large cylinder is above it. The design is 
completely symmetrical; it has the important mechanical ad- 
vantage of dispensing with coupling rods, while retaining the 
greater tractive power of four drivers ; only one axle is cranked, 
and that with a single crank in the centre, which leaves ample 
room for long bearings. 

232. Tramway and Road Iiocomotives. Tramway loco- 
motives for the most part resemble railway locomotives in the 
general features of their design. The boiler is of the usual 
locomotive type. A pair of cylinders in front, either inside or 
outside the frames, are connected directly to the hindmost of two 
coupled driving axles. Owing to the smallness of the driving- 
wheels the axles lie near the road, and the cylinders are set 
sloping at a considerable angle upwards away from the cranks to 
keep them clear of dirt. To prevent the discharge of steam into 
the atmosphere, the exhaust steam is often led into an atmo- 
spheric condenser, consisting of a large number of pipes placed on 
the top of the engine, and exposed to free contact with the air. 
In some instances the common locomotive type is widely departed 
from : a mixed vertical and horizontal boiler is used, and the engine 
is connected to the driving axle by worm-wheel or other gear, or 
by a rocking lever between the connecting-rod and the cranks 

In the "fireless" tramway locomotive of Mr. L^on Francq, 
a reservoir which takes the place of an ordinary boiler is 
charged at the beginning of the journey with water heated under 
pressure by injecting steam from stationary boilers at a pressure 

1 See Min, Proc. Inst. 0.^., vol xxix., 1884 ; also Proc. In$t. Mech. Eng.^ 1880. 


of 15 atmospheres. The thermal capacity of the water is suflScient 
— without further addition of heat — to supply steam to the 
engine during the journey, at a pressure which gradually feUs oflP. 
The system has not come into general use. 

Several forms of tramway engine have been devised in 
which the motive power is supplied by compressed air*. In the 
Mekarski system the compressed air, on its way from the reservoir 
to the cylinders, passes through a vessel containing hot water and 
steam under pressure (charged, as in Francq*s system, by injecting 
steam at a station). In this way the air is heated, and may then 
expand in the cylinder without having its temperature lowered to 
an objectionable degree. 

Steam road-locomotives or traction-engines have usually a 
boiler of the locomotive type, with a cylinder or compound pair 
of cylinders, generally on the top, driving a shaft from which 
motion is taken by a gearing chain or spur-wheels to a single 
driving axle at the fire-box end. The engine is steered by means 
of a leading axle, whose direction is controlled by a hand-wheel 
and chain-gear. To facilitate rapid turning the driving-wheels 
are connected to their axle by a diflferential or compensating gear 
which allows them to revolve at diflferent speeds. This is a set 
of four bevel-wheels like White's dynamometer coupling: the 
outside bevel-wheels are attached to the driving-wheels; the 
intermediate ones, which gear with these, turn in bearings in a 
revolving wheel driven by the engine. So long as both driving- 
wheels are equally resisted both are driven at the same speed, but 
if one is retarded (as the inner wheel is in going round a curve) it 
acts to some extent as a fulcrum to the bevel gear, and the outer 
wheel takes a greater share of the motion. 

An important feature in traction-engines is the elasticity of 
the driving-wheels. Many devices have been employed, partly to 
give the wheels an extended tread, or arc of contact with the 
ground, and partly to avoid shocks in passing over rough ground*. 
In some designs the rims have been made elastic, as in 
Mr R. W. Thomson's road steamer, where each wheel had a 
thick tyre of india-rubber, protected on the outside by an armour 
of small plates. In others the spokes have had the form of 

1 Proe, Inst, Mech. Eng., 1879. » Proe, Inst, Mech, Eng., 1878, 1881. 

» Min. Proc, IruU C.E., vol. zxzvi., 1873; vol. oiii., 1890. 



springs allowing the axle to take an eccentric position. In others 
still the framework of the wheel is nearly rigid, but the circum- 
ference is filled with blocks of wood which are held in cells with 
an elastic pad behind each, so that each block in turn is pushed 
in when it becomes part of the surface over which the weight is 
distributed, and the tread of the wheel is consequently enlarged. 



233. Air and Gas-engines with external or internal 
combustion. Under this head we have to include all heat- 
engines in which the working substance is air, or the gaseous 
products of the combustion of fuel and air, whether the fuel be 
itself solid, liquid, or gaseous. When air alone forms the working 
substance, it receives heat from an external furnace by conduction 
through the walls of a containing vessel, just as the working 
substance in the steam-engine takes in heat through the shell of 
the boiler. An engine supplied with heat in this way may be 
called an eaternal-combustion engine, to distinguish it from a very 
important class of engines in which the combustion which supplies 
heat occurs within a closed chamber containing the working 
substance. The ordinary coal-gas explosive engine is the most 
common type of intern(d'C(>mbu8tion engine. 

Compared with engines using saturated steam, air and gas- 
engines have the important advantage that the temperature 
and the pressure of the working substance are independent of one 
another. In the steam-engine, and in any other heat-engine in 
which the working substance is a saturated vapour, the upper limit 
of temperature is comparatively low in consequence of the high 
pressure with which high temperature is, in such cases, necessarily 
associated. But in an air or gas-engine it becomes possible to use 
an upper limit of temperature greatly higher than the limit in the 
ordinary steam-engine, and if the lower limit is not correspondingly 
raised an increase of thermodynamic efficiency results. It is true 
that the same advantage might be obtained in the case of steam, 
by excessive superheating ; but this would mean substantially the 
conversion of the engine into the type we are now considering, the 
working substance being then steam gas. 


So long as external combustion is used, there must still be 
some considerable drop in temperature, of an irreversible and 
therefore wastefiil kind, between the temperature which is pro- 
duced by combustion in the furnace, and the temperature at which 
the working air receives its heat, since without this no sufficiently 
rapid conduction of heat through the walls of the heater could 
occur. Internal combustion engines have the advantage that the 
temperature which is produced in the combustion is itself the 
upper limit in the thermodynamic cycle. 

234. Air-engine using Oamot's cycle. A simple, thermo- 
djniamically perfect form of external-combustion air-engine would 
be one following Camot's cycle, in which heat is received while 
the air is at the highest temperature Ti, the air meanwhile 
expanding isothermally. After this the supply of heat is stopped, 
and the air is allowed to expand adiabatically until its temperature 
falls to the lower extreme xg. At this it is compressed isother- 
mally, giving out heat, and finally the cycle is completed by 
adiabatic compression, which restores the initial high temperature 
Ti. The indicator diagram for this cycle has been sketched in 
fig. 12, § 41. Practically, this action would be attended by the 
serious drawback that the volume to be swept through by the 
piston would be very great in relation to the work. done. The 
inclination of adiabatic to isothermal curves for a gas is slight, 
and hence the area of the diagram, or the eflfective work done per 
revolution, is small in comparison with the two quantities of which 
it is the diflference, namely, the work done by the substance during 
the forward stroke and the work spent upon it during the backward 
stroke. An air-engine using Camot's cycle would consequently be 
excessively bulky and mechanically inefficient. 

235. External Combustion Air-engine with Regene- 
rator: Stirling, Ericsson. This objection is much lessened 
when the use of a regenerator (§ 51) is substituted for the 
adiabatic steps of the Camot cycle. In Stirling's engine, where 
the regenerator was first used, the working substance was cooled 
from the upper limit Ti to the lower limit r^ by passing in one 
direction through a regenjerator, which stored the heat it extracted 
from the gas in such a way that when the gas was passed through 
the regenerator in the opposite direction the heat was again taken 
up and the temperature consequently rose from Ts to Tj. The 


cycle of operations has been described in § 52 and an ideal 
indicator diagram has been sketched in fig. 13. 

Fig. 176. Stirling's Air-engine. 

Several forms of engines were designed by Stirling in which 
the action approximated to the cycle of § 52. The characteristic 
parts of one of them are shown in section in fig. 176. A is the 
heater, a closed iron vessel containing air, externally heated by a 
furnace beneath it. A pipe from the top of A leads to the 
working cylinder B, At the top of J. is a refiigerator (7, consisting 
of pipes through which cold water circulates. In A there is a 
displacer plunger D, which is driven by the engine ; when this is 
raised the air in J. is in the lower part of the vessel and is conse- 
quently taking in heat fi-om the furnace, whereas when 2) is lowered 
the air in -4 is transferred from the lower to the upper part and 
is thereby brought into contact with the refrigerator. On its way 
from the bottom to the top of J., or from the top to the bottom, 
the air must pass through an annular lining of wire-gauze E, 


This is the regenerator, and the air in passing up through it 
becomes cooled, and in passing down again through it becomes 
heated. At the beginning of the cycle D is at or near its highest 
position. The air is then receiving heat at temperature Ti, and 
is expanding isothermally ; this is the first stage in § 52. Then 
the plunger D descends. The air is driven through the regenerator, 
where it deposits heat, and its temperature on emerging at the 
top is Tj. Next, the working-piston makes its down-stroke (in the 
actual engine the working cylinder was double-acting, another 
heating vessel, precisely like A, being connected with the cylinder 
B above the piston); this compresses the air isothermally, the 
heat produced by compression being taken up by the refrigerator 
C Finally the plunger is raised, and the working air again passes 
down through the regenerator, taking up the heat it left there, and 
rising in temperature to Ti. 

The actual forms in which Stirling's engine was used are 
described in two patents by R. & J. Stirling (1827 and 1840^). 
An important feature in them was that the air was compressed by 
means of a pump which formed an additional organ of the engine, 
80 that its average pressure was kept much above that of the 
atmosphere. Stirling's cycle is theoretically perfect whatever be 
the density of the working air, and compression does not in its 
case increase what may be called the theoretical thermodynamic 
efficiency. It does, however, very greatly increase the mechanical 
efficiency, and also> what is of special importance, it increases the 
amount of power developed by an engine of given size. To see this 
it is sufficient to consider that with compressed air a greater 
amount of heat is dealt with in each stroke of the engine, and 
therefore a greater amount of work is done. Practically com- 
pression also increases the thermodynamic efficiency by reducing 
the ratio of the heat wasted by external conduction and radiation 
to the whole heat. 

A double-acting Stirling engine of 50 I.H.P., used in 1843 at 
the Dundee foundry, appears to have realized an efficiency of 0*3, 
and, notwithstanding very inadequate means of heating the air 
it consumed only 1*7 lb. of coal per i.-H.-P.-hour I This engine 

^ The 1827 patent is leproduced in Fleeming Jenkin'a Lecture on Gas and 
Caloric Engines, InsU Civ. Eng., Heat Lectures, 1883 — 84. See also Min, Proc. 
Inst. C. E., 1845 and 1854. 

^ See Bankine's Steam-Engine ^ p. 867. The consumption per brake h.-p. was 
much greater. 


remained at work for three years, but was finally abandoned on 
account of the failure of the heating vessels. In one form of 
the engine as described Stirling's patent the regenerator was a 
separate vessel ; in another the plunger D was itself constructed 
to serve as regenerator by filling it with wire-gauze and leaving 
holes at top and bottom for the passage of the air through it. 

Another mode of using the regenerator was introduced 
in America by Ericsson, in an engine which also failed, partly 
because the heating surfaces became burnt, and partly because 
their area was insufficient. In Ericsson s engine, which was tried 
on a considerable scale on the steam-ship " Caloric," the tempera- 
ture of the working substance was changed by passing through the 
regenerator while the pressure remained constant. Cold air was 
compressed by a pump into a receiver, fi-om which it passed 
through a regenerator into the working cylinder. In so passing it 
absorbed heat from the regenerator and expanded. The air in 
the cylinder was then allowed to expand further by taking in heat 
fi'om a furnace under the cylinder until its pressure fell to near 
that of the atmosphere. The cycle was completed by the discharge 
of the air through the regenerator. The indicator diagram ap- 
proximates to a form bounded by two isothermals and two lines 
of constant pressured 

236. Modem Air-engines of the Stirling type. Exter- 
nally-heated air-engines are now employed only for very small 
powers — from a fraction of 1 H.-P. up to about 3 H.-P. Powerful 
engines of this type are scarcely practicable, partly on account of 
the relatively enormous bulk they would have and partly on 
account of the difficulty which would be experienced in the 
heating of large quantities of air. By keeping the working sub- 
stance highly compressed, giving it a mean density much in excess 
of that of atmospheric air, the bulk of the working cylinder and 
displacer might be reduced, but the difficulty would remain of 
getting enough heating surface and of preserving the heater from 
being burnt through its exposure to oxygen at a high temperature. 
The small engines of this tjrpe that are now manufactured 
resemble the original Stirling engine very closely in the main 
features of their action, and comprise essentially the same organs. 

One of these modem Stirling engines is the small domestic 

^ For a diagram of Ericsson's engine see Bankiue's Steam-Engine, or Proc, Inst, 
Meeh. Eng,, 1S78. 



motor manufactured under the patents of Mr H. Robinson (fig. 177). 
In this case there is no compressing pump and the mean pressure 
of the working air is equal to the pressure of the atmosphere. 

Fio. 177. Bobinson's form of Stirling Engine. 

The range of pressure is slight — so slight indeed that no packing 
is needed in the piston or other working parts — and the engine 
developes only a fraction of one horse-power. 

A is the heater and displacer cylinder ; B is the working cylin- 
der, which communicates with -4 by a passage D, A is heated 
externally by a small coke fire at (7 or by a gas flame from 
a Bunsen burner. The displacer E takes its motion fi:om a 
rocking lever F connected by a short link to the crank-pin, and is 
about 90° in phase ahead of the working piston. In the figure the 
displacer is at the bottom of its stroke and the piston has still 
half the back stroke to perform. The displacer E is itself the 
regenerator, its construction being such that the air passes up and 
down through it as in one of the original Stirling forms. On the 



top of the displacer cylinder is a water vessel G, which is the 
refrigerator, and this is kept in communication with the circulating 
water tank H. The account which has already been given of the 
Stirling cycle will serve as a description of the action in this 
engine. A conspicuous feature is that there are neither valves, 
packing, nor glands ; but the absence of compression, which makes 
this possible, limits the eflficiency of the engine as well as its power. 
A larger engine of the Stirling type, working up to some 3 
horse-power, is made by Messrs Bailey, of Salford. Another, the 
Rider engine, made by Messrs Hayward and Tyler, follows sub- 

FiG. 17S. Bider*8 Hot Air Engine. 


stantially, but not exactly the Stirling cycle. A sectional view of 
this engine is given in fig. 178. A and B are two cylinders, 
open at the top, with plunger pistons C and D, which are connected 
to cranks nearly at right angles. Between the two is the re- 
generator H. Round the lower part of (7 is the refrigerator E, a 
jacket through which cold water is kept circulating. Under the 
lower part of £ is the furnace F which heats the air contained in 
the space below the plunger D. In the position shown in the 
figure, D is rising, and C is just beginning to rise. Nearly all the 
working air has been compressed into G and is expanding as it 
takes in heat, doing work against the plunger D and also against C. 
By the time D reaches the top of its stroke C is about half way 
up : air is passing rapidly through the regenerator from G to the 
space under (7, and is cooled first by the regenerator and then by 
the water-jacket E. As D comes down this transfer of the air 
continues and the pressure falls. Then C follows, compressing the 
air beneath it while the refrigerator E absorbs the heat, and finally 
forcing all the working air back through the regenerator into the 
heater, when the cycle begins again. The maximum pressure 
reached during the cycle is about 20 lbs. per sq. inch. 

The action is of courae continuous, but we may broadly 
distinguish the following four stages: 

(1) The air, previously compressed to a small volume (in 6r), 
takes in heat at its highest temperature and expands, doing work 
on D and subsequently to some extent on C. 

(2) After this expansion it is transferred through the regene- 
rator to the cold cylinder A, storing heat in the regenerator and 
losing pressure. During this process little work is done on or by 
the air, since the actions on the plungers nearly balance. In other 
words, the volume does not materially change. 

(3) The air which is now in A, expanded to large bulk and at 
a low temperature, is compressed by the descent of G and gives 
out heat to the refrigerator. During this process work is done 
upon the air by the fly-wheel. 

(4) The compressed air is transferred through the regenerator 
to G, rising in temperature and pressure. In this process, again, 
little work is done by or on the air. 

This engine differs from the pure Stirling type chiefly in having 
a displacer which is also a working piston. The Rider engine is 
mainly used to pump water for domestic supply, and the refrige- 


rator jacket is kept cool by making the water which the engine 
pumps circulate through it. 

237. Internal Combustion Air-engines. The earliest 
practical example of the internal combustion engine (if we leave 
guns out of account) appears to have been the hot-air engine of 
Sir George Cayley^ of which Wenham's* and Buckett's'^ engines 
are recent forms. In these engines coal or coke is burnt under 
pressure in a closed chamber, to which the fuel is fed through a 
species of air-lock. Air for combustion is supplied by a com- 
pressing pump, and the engine is governed by means of a 
distributing valve which supplies a greater or less proportion of 
the air below the fire as the engine runs slow or fast. The 
products of combustion, whose volume is increased by their rise in 
temperature, pass into a working cylinder, raising the piston. 
When a certain fraction of the stroke is over the supply of hot gas 
is stopped, and the gases in the cylinder expand, doing more work 
and becoming reduced in temperature. During the return stroke 
they are discharged into the atmosphere, and the pump takes in a 
fresh supply of air. Fig. 179 is a diagram section of the Buckett 
engine. A is the working piston, the form of which is such as to 
protect the tight sliding surface (at the top) from contact with the 
hot gases ; B is the compressing pump, and C is the valve by which 
the governor regulates the rate at which fuel is consumed by admit- 
ting more or less of the air under the grate through the channel F. 
D is the air-lock and hopper through which ftiel is supplied, and E 
is the exhaust valve through which the products of combustion are 
finally expelled. 

In engines of this class the degree to which the action is 
thermodynamically efficient depends very largely on the amount 
of cooling the gases undergo by adiabatic or nearly adiabatic 
expansion under the working piston. Without a large ratio of 
expansion the thermodynamic advantage of a high initial tempe- 
rature is lost. In any kind of internal combustion engine the 
gases have to be discharged at atmospheric pressure, and con- 
sequently a large ratio of expansion is possible only when there is 
much initial compression. Compression is therefore an essential 

^ Niehol8on*$ Art Journal, 1807. 
» Proc, Irut. Meek, Eng,, 1878. 
> Fleeming Jenkin, loe, eit. 



condition, without which a heat-engine of this type cannot be 
made efficient. It is also, as has abeady been pointed out, an essen- 
tial feature in any aii'-engine which is to develope a fair amount of 
power without excessive bulk. 

Fia. 179. Buckett's Internal Combustion Air-Engine. 

Internal combustion engines using solid fuel have hitherto been 
but little used, and that only for small powers. But the use of 
liquid and especially of gaseous fuel has given the internal 
combustion engine a position of great and constantly increasing 
importance. Gas-engines, that is to say, engines acting by the com- 
bustion or explosion of a mixture of air and combustible gas have 
in recent years entered into serious competition with the steam- 
engine. In most of these the fuel is ordinary coal-gas ; it may 
however be a cheaper combustible gas, such as that produced by 
Mr Dowson's process ; and in a number of modem examples of the 
internal combustion engine the fuel is petroleum, generally va- 
porised before its admission to the cylinder in which combustion 
is to occur. 


238. Early Oas-engines. The first gas-engine to be 
brought into practical use was that of Lenoir (1860) \ During 
the early part of the stroke air and gas, in proportions suitable for 
combustion, were drawn into the cylinder. At about half-stroke 
the inlet valve closed, and the mixture was immediately exploded 
by an electric spark. The heated products of combustion then 
did work on the piston during the remainder of the forward 
stroke, and were expelled during the back stroke. The engine 
was double-acting, and the cylinder was prevented from becoming 
excessively heated by a casing through which water was kept 
circulating. This water-jacket is a feature that has been retained 
in nearly all later gas-engines. 

An indicator diagram from a Lenoir engine is shown in 

fig. 180*. After the explosion the line falls, partly from expansion, 

and partly from the cooling action of 

the cylinder walls ; on the other hand, 

its level is to some extent maintained 

by the phenomenon of after-burning, 

which will be discussed later. In this „ ton t ' • ^ • r.- 

Fm.lSO. Lenoir Engine Diagram. 

engine, chiefly because there was no 

compression, the heat removed by the water-jacket bore an 
exceedingly large proportion to the whole heat. The efficiency 
was comparatively low both on this account and on account of the 
limited range through which the heated products of combustion 
were allowed to expand. About 95 cubic feet of gas were used 
per horse-power-hour, which is nearly four times as much as a 
good modem gas-engine consumes. Hugon's engine, introduced 
five years later, was a non-compressive engine very similar to 
Lenoir's. A novel feature in it was the injection of a jet of cold 
water to keep the cylinder from becoming too hot. These engines 
are now obsolete; the type they belonged to, in which the 
mixture is not compressed before explosion, is now represented by 
one small engine — Bischoffs — ^the mechanical simplicity of which 
atones for its comparatively wasteful action in certain cases where 
but little power is required. 

In 1866 Otto and Langen introduced a curious engine', 

1 For a fuU acoonnt of the early history of the gas-engine as weU as for 
descriptions of numerous modem forms see DonMn's Text-hooh of Qas^ Oily and Air^ 
engines (1894). 

> Slade, Jowm, Franklin Inst., 1866. > Proc, Inst. Meeh, Eng., 1875. 


which, as to ecoDomy of gas, was distinctly superior to its 
predecessors. Like them it did not use compression. The 
explosion occurred early in the stroke, in a vertical cylinder, under 
a piston which was free to rise without doing work on the engine 
shaft. The piston rose with great velocity, so that the expansion 
was much more nearly adiabatic than in earlier engines and the 
ratio of expansion was greater. After the piston had reached the 
top of its range the gases became further cooled by giving up heat 
to the walls of the cylinder, and, their pressure being below that 
of the atmosphere, the piston came down, this time in gear with 
the shaft, and doing work upon it. The burnt gases were dis- 
charged during the last part of the down-stroke. A fnction- 
coupling allowed the piston to be automatically thrown out of gear 
with the shaft when rising, and into gear when descending. This 
"atmospheric" gas-engine used about 40 cubic feet of gas per 
horse-power-hour, and came into somewhat extensive use in spite of 
its noisy and spasmodic action. After a few years it was displaced 
by a greatly improved type, in which the direct action of Lenoir's 
engine was restored, but the gases were compressed before ignition. 

The four-stroke cycle of Beau de Rochas and Otta 

The advantage of compressing the explosive mixture before igniting 
it in order to make the subsequent expansion large, appears to 
have been first pointed out by Beau de Rochas, who in a French 
patent of 1862 indicated the limit which is imposed in compression 
by the elevation of temperature causing the mixed gas to explode, 
and suggested a means of carrying out the process without 
using a separate compressing pump. His plan was to have the 
following four operations take place, on one side of the working 
piston, during four successive strokes or two revolutions of the 

(1) Drawing in the charge of gas and air during one whole 
stroke of the piston. 

(2) Compression during the return stroke (into a compara- 
tively large clearance space below the piston). 

(3) Ignition at the dead point, followed by expansion during 
the third stroke. 

(4) Discharge of the burnt gases from the cylinder during 
the fourth and last stroke. 

This " four-stroke " cycle of operations is now used in almost 


all gas-engines. Beau de Rochas further pointed out that, besides 
compression, high speed and small cylinder surface were conditions 
to be aimed at as favourable to economy. Extremely valuable as 
were the suggestions contained in his patent they were for a long 
time unproductive. It was not till 1876 that Dr Otto, who had 
reinvented the Beau de Rochas four-stroke cycle, introduced the 
highly successful gas-engine in which this action is carried out. 
The Otto " silent " engine (so called to distinguish it from its noisy 
predecessor, the engine of Otto and Langen) not only was the first 
gas-engine to come widely into use, but has formed the model to 
which, since the expiry of Otto's master patent, other gas-engines 
are for the most part indebted for the chief features of their action. 
The manufacture of the Otto engine in England by Messrs Cross- 
ley led to its rapid introduction in thousands of cases where the 
greater cost of fuel, as compared with a steam-engine, was more 
than balanced by the greater convenience and economy in respect 
of attendance of the new motor. It should be added that 
illuminating coal-gas — the usual fuel of these engines — is a more 
costly fuel than there is any need to use in a gas-engine, and is in 
fact used only because it is readily obtainable. Much cheaper com- 
bustible gases, destitute of illuminating power, will serve the pur- 
poses of the gas-engine ; and when gas-engine power is used on a 
large scale, it is worth while to put down the plant necessary for 
the manufacture of cheap gas. This, in fact, is often done, and 
under such conditions the cost of fuel in the gas-engine compares 
favourably with the cost of fuel in the steam-engine. 

240. The Otto Engine. In the Otto engine, and in many 
other forms which resemble it, the cylinder is single acting, with 
a trunk piston, and the explosive mixture is compressed before 
ignition into a large clearance space at the back end of the 
cylinder. The volume of the clearance is sometimes less than 
half the volume through which the piston sweeps, but is often 
more than half that volume. To complete the action requires 
two revolutions of the crank-shaft. 

During the first forward stroke gas and air are drawn in by 
the piston. During the first back-stroke the mixture is com- 
pressed into the clearance space. The mixture is then ignited 
as the crank reaches the dead point, and the second forward 
stroke (which is the only working stroke in the cycle) is per- 
£. 24 


formed under the pressure of the heated products of combustion. 
During the second back-stroke the products are discharged into the 
atmosphere through an exhaust valve, with the exception of so 
much as remains in the clearance space, which serves to dilute the 
explosive mixture in the next cycle. The cylinder is kept cool 
enough to admit of lubrication, by means of a jacket through 
which a continuous circulation of water is kept up. The admission 
and exhaust valves are worked by a shaft which is geared to run 
at half the speed of the crank-shaft, so that their period is double 
that of the piston. In early forms of the Otto engine the ignition 
of the compressed gases was effected by carrying a flame, through a 
narrow port in a slide-valve, from a gas jet that was kept burning 
outside to the mixture within. To prevent the' gases firom 
blowing back through the valve when the explosion took place the 
slide was arranged so that the port in it which served as a vehicle 
for the flame had passed under a cover which shut it off from the 
atmosphere, before it reached the fixed port on the cylinder cover 
through which the flame passed in to ignite the contents of the 
cylinder. This mode of igniting the gases is now generally aban- 
doned and an ignition tube is used instead. This is a small closed 
tube which is maintained at a bright red heat by a flame playing 
on its outside surface, while a portion of the explosive mixture is 
allowed to enter the tube from the cylinder at the time when it 
should be fired. In most cases a valve opens to allow the 
contents of the cylinder access to the ignition tube, but in some 
modem gas-engines this " timing valve " is dispensed with and the 
ignition tube is in free communication with the cylinder through- 
out, the contents becoming fired only when their pressure is raised 
by the back-stroke of the piston, an arrangement which tends to 
make the instant of ignition rather uncertain. In a few gas- 
engines electrical means of firing are retained: thus in the 
"Simplex," a successful French engine, a continuous stream of 
sparks is kept up, generated by a battery and induction coil in a 
small chamber in the cover of a slide-valve which serves as a 
timing valve to let the sparks take effect at the proper time, by 
giving the explosive mixture access to the spark chamber. 

The speed of a gas-engine is usually regulated by a centrifugal 
governor, which cuts off the supply of gas when the speed exceeds 
a certain limit, making the engine miss one or more explosions. 
The governor determines whether the gas valve shall or shall not 


be opened, by means of a " hit and miss " arrangement. In some 
small engines of recent construction the inertia of a reciprocating 
piece is used instead of the inertia of revolving pieces to determine 
the admission or non-admission of gas. 

241. Other Gas-engines. The Otto, or Beau de Rochas 
cycle, is now so generally adopted that comparatively little 
interest attaches to the modes of action introduced in other 
tj^es of gas-engine, which after attaining some vogue have 
for the most part failed to maintain their position. Mi Dugald 
Clerk, whose experiments have been of great service ii;i clearing 
up disputed points in gas-engine theory, introduced in 1880 a 
motor in which the explosion took place at each forward stroke 
of the piston, instead of at each alternate forward stroke as in 
Otto's. The gas and air were inhaled by an auxiliary piston in 
s, separate cylinder, frotn which they were delivered to the main 
cylinder just after the main piston had completed its working 
stroke. They entered through a trumpet mouth or large cone 
forming the cover at the back end of the cylinder, which had the 
effect of removing the kinetic energy of the stream and hence of 
allowing the fresh gases to enter without intermingling much 
with the products of combustion already in the cylinder. The 
fresh charge drove the products of combustion in front of it, 
causing these to be expelled at exhaust ports in the side of the 
cylinder close to the front end of the stroke. The piston, re- 
turning, closed these exhaust ports and compressed the fresh 
mixture, which was ignited as usual when its compression was 
completed by the piston passing its dead-point at the back end\ 
The indicator diagram was almost identical with that given by 
the Otto engine. 

It is a defect of the ordinary Otto cycle that the ratio in which 
the gases are expanded after ignition is no greater than the ratio 
in which the explosive mixture is compressed. A larger ratio of 
expansion is desirable, for the temperature and the pressure are 
still high when release occurs. The ingenious "differential" 
engine of Mr Atkinson (1885) was an attempt to avoid this 
drawback. Its working chamber consisted of the space between 
two pistons working in one cylinder. During exhaust the pistons 
came close together; they receded from each other to take in a 

I See Mr Clerk's book, ** The Gas-Engine,** 18S6. 



fresh charge ; they approached for compression ; and finally they 
receded again very rapidly and farther than before, after ignition 
of the mixture, thus giving a comparatively large ratio of ex- 
pansion with the further advantage that the working stroke took 
place fast. At the same time, by moving bodily along through 
the cylinder, the pistons uncovered admission and exhaust ports 
in the sides, as well as an ignition tube which was kept perma- 
nently incandescent. The pistons were connected to a single 
crank-pin through a pair of beams or levers with connecting links 
at each end ; this had the important disadvantage of introducing 
a large number of working jointa 

A year or so later Mr Atkinson abandoned the use of two 
pistons, but succeeded in giving a single piston long and short 
strokes alternately, by connecting it to the crank-pin through a 
species of toggle joint which made two complete oscillations for 
each revolution of the shaft. The first oscillation served to inhale 
and compress the gases ; the second, the amplitude of which was 
about twice as great, served for the working and exhausting stroke. 
Competitive tests made under the auspices of the Society of Arts 
showed that the " cycle " engine, as this form was called, had an 
exceptionally high efficiency, but the mechanical complication of 
the toggle with its still numerous joints has stood in the way of 
its success. 

In an engine made by Messrs Dick, Kerr and Co., a double- 
acting stroke is used, with explosions on both sides of the piston 
alternately. In the original form of this engine (the " Griffin ") 
there was what is called a scavenging stroke (or rather two 
strokes) in addition to the essential parts of the Otto cycle. After 
the products of combustion had been expelled iD the fourth stroke 
of the ordinary cycle a fifth and sixth stroke were occupied in 
drawing in and expelling air from the cylinder, to sweep it clear 
of the products of combustion before the next charge should be 
admitted. In the more recent form of double-acting engine the 
scavenging strokes are omitted and the usual four-stroke Otto 
cycle is adhered to without change, the result of the double 
action being that two impulses are secured in every two revolutions 
of the shaft. Gas-engines have been made by these makers to 
indicate as much as 600 horse-power. 

In one or two other forms of gas-engine the fix)nt or idle side of 
the piston is utilized to serve as a displacer, acting like the separate 


displacer of the Clerk engine to inhale a mixture of gas and air 
into a chamber which in some cases encloses the connecting-rod 
and crank. The mixture then passes to the back or working end, 
while the burnt products of the previous stroke are driven out 
before it, and is then compressed and exploded ; the result being 
that an explosion is secured at each instead of each alternate 
revolution. The cycle is substantially Otto's, but with its chief 
mechanical imperfection removed, namely, the idle revolution. 

242. Action in the cylinder of the Otto Engine. If the 

explosion of a gaseous mixture were practically instantaneous, 
producing at once all the heat due to the chemical reaction, and if 
the expansion and compression were adiabatic, the theoretical 
indicator diagram of an engine of the Otto type would have the 
form shown in fig. 181. OA represents the 
volume of clearance ; AB is the admission, 
at atmospheric pressure ; BG is the com- 
pression (which is assumed in the sketch to 
be adiabatic) ; CD is the rise of pressure 
caused by explosion; DE is adiabatic 
expansion during the working stroke; 
and EBA is the exhaust. The height of 
the point D above G may be calculated 

when we know the temperature at G (an element of considerable 
uncertainty in practice), as well as the specific heat (at constant 
volume) of the burnt mixture, the amount of heat evolved by the 
explosion, and the change of specific density due to the change 
of chemical constitution which explosion brings about. With the 
proportion of coal-gas and air ordinarily employed the change of 
specific density may generally be neglected, as the volume of the 
products would diflfer by less than 2 per cent, from the volume 
of the mixture before explosion if both were reduced to the same 
pressure and temperature. 

The rise of pressure which actually takes place in the 
indicator diagrams of gas-engines when the mixture is ignited is 
found to be in all cases much less than the calculated rise of 
pressure which would be caused by a strictly instantaneous 
explosion. An actual diagram from an Otto engine working in 
its normal manner is given in fig. 182, where the reference 
letters distinguish the parts of a complete cycle, as in fig. 


181. It shows a rapid rise of pressure on explosioD, so rapid 
that the volume has not very materially altered when the 
maximum of pressure is reached; and the specific heat at 

A >• B 

Fio. 182. Actual indicator diagram from an Otto gas-engine. 

constant volume may therefore be used without serious error in 
calculating the amount of heat which this rise accounts fon 
When this calculation is madeS it turns out that only about 60 or 
70 per cent, of the potential heat of combustion in the mixture is 
required to produce the rise of temperature which corresponds to 
the rise of pressure to the highest point of the curve, namely fix>m 
C to D, The remainder of the heat continues to be slowly evolved 
during the subsequent expansion of the hot gases. The process of 
combustion — a term evidently more appropriate than explosion — 
is essentially gradual ; when ignition takes place it begins rapidly, 
but it continues to go on at a diminishing rate throughout the 
whole or nearly the whole of the stroke. That part which takes 
place after the maximum pressure is passed constitutes the pheno- 
menon of " after-burning " to which allusion has been made above, 

243. After-burning. The existence of after-burning is 
proved not only by the fact that the maximum pressure after 
ignition is much less than it would be if combustion were then 
complete, but also by the form which the curve of subsequent 
expansion takes. During expansion the gases are losing much 
heat by conduction through the cylinder walls. The water-jacket 
absorbs about 40 or in some cases even 50 per cent, of the whole 

^ See two papers by Mr Dagald Clerk, **0n the Theory of the Gas-Engine," and 
**0n the Explosion of Homogeneous Gaseons Mixtures," Min. Proc, Inst, C,E., 
1882 and 1886. 


heat developed in the engine \ and the greater part of this is of 
course taken up from the gases during the working stroke. Not* 
withstanding this loss of heat, the curve of expansion does not fall 
much below the adiabatic curve ; in some tests indeed it has been 
found to lie higher than the adiabatic curve. This shows that the 
loss to the sides of the cylinder is being made up by continued 
development of heat within the gas. The process of combustion 
is especially protracted when the explosive mixture is weak in 
gas; the point of maximum pressure then comes late in the 

A =5= ; s 

Fio. 183. Otto Engine diagram with weak explosive mixture. 

stroke ; and it is probable that the products which are discharged 
into the exhaust contain some incompletely burnt fuel. Fig. 183 is 
the indicator diagram of an Otto engine supplied with a mixture 
containing an exceptionally large proportion of air: it exhibits 
well the very gradual character of the combustion in such a case. 

The process of explosive combustion has been examined in the 
experiments already referred to of Mr Clerk, who exploded mixtures 
of gas and air, and also mixtures of hydrogen and air, in a closed 
vessel furnished with an apparatus for recording the time-rate of 
variation of pressure. In these experiments the pressure fell after 
the explosion only on account of the cooling action of the 
containing walls. The temperature before ignition being known, 
it became possible to calculate from the diagrams of pressure the 
highest temperature that was reached during combustion (on the 
assumption that the specific heat of the gases remained unchanged 
at high temperatures), and to compare this with the temperature 
which would have been produced had combustion been at once 
complete. Mixtures of gas and air were exploded, the proportion 
of gas varying from -^ to ^, and the highest temperature produced 

^ Clerk, loc, cit. Also, Brooks and Steward, Van Nostrand^s Eng, Mag,, 1S83; 
Ayrton and Perry, Phil. Mag,, July 1884; Slaby, Beport quoted in F. Jenkin*s 
Lecture, Inst. G.E., 1884, and other trials quoted by Mr Bonkin. 


was generally a little more than half that which would have been 
reached by instantaneous combustion of the mixture. With the 
best proportion of coal-gas to air (1 to 6 or 7) the greatest 
pressure and hottest state was found one-twentieth of a second 
after ignition, and the temperature was then ISW C, — ^instead of 
3800° C, which would have been the temperature had all the heat 
been at onc6 evolved. With the weakest mixtures about half a 
second was taken to reach a maximum of temperature, and its value 
was 800° C, instead of 1800° C. In this case, however, the degree 
of completeness of the combustion is not fairly shown by a com- 
parison of these temperatures, since much cooling occurred during 
the relatively long interval that preceded the instant of greatest 

To explain the phenomenon of after-burning or delayed 
combustion, it has been supposed that the high temperature to 
which the gases are raised in the first stages of the explosion 
prevents union from being completed, — just as high temperature 
would dissociate the burnt gases were they already in' chemical 
union, — until the fall of temperature by expansion and by the 
cooling action of the cylinder walls allows the process of union to 
go on. The maximum temperature attained in the gas-engiue is 
high enough to cause a perceptible amount of dissociation of the 
burnt products ; it may therefore be admitted that this explana- 
tion of delayed combustion is to some extent, valid. On the other 
hand, the phenomenon is most noticeable with mixtures w^eak in 
gas, in which the maximum temperature reached is low, and the 
dissociation effect is correspondingly small. It appears, therefore, 
that dissociation is not the main cause of the action ; apart from 
it the process of combustion of a gaseous mixture is gradual, 
beginning fast and going on at a continuously-diminishing rate as 
the combustible mixture becomes more and more diluted by the 
portions already burnt. If the mixture is much diluted to begin 
with, the process is comparatively slow from the first. 

Much stress was at one time laid by Otto on the desira- 
bility of having a stratified mixture of gases in the cylinder, 
with a part rich in gas near the ignition port and a greater 
proportion, of residual products or air near the piston. It has even 
been supposed that stratification of the gases is the cause of their 
gradual combustion. Mr Clerk's experiments are conclusive 
against this ; the mixtures he used, which gave in some cases very 


gradual explosions, were allowed to stand long enough to become 
sensibly homogeneous. In dealing with weak mixtures it is no 
doubt of advantage to have a small quantity richer in fuel than 
the average close to the igniting port to start the ignition of the 
rest, — but beyond this stratification has probably no value. In 
the ordinary working of a gas-engine it is evident that no general 
stratification can occur, when account is taken of the commotion 
which the air and gas cause as they rush into the cylinder at a 
speed exceeding that of an express train, except in cases where 
special precautions are taken to deprive the gases of kinetic 
energy on their entry, as in Clerk's engine, where the gases were 
reduced to stillness by means of an expanding cone in order that 
the fresh charge should not mix with the products of the previous 

244. Performance of OaB-engines. A gas-engine of the 
Otto type using illuminating coal-gas as fuel bums from 20 to 25 
cubic feet per indicated horse-power-hour. In a few instances the 
consumption is slightly under 20 cubic feet, but this is exceptional. 
The mechanical eflSciency in favourable cases 0*85 ; in other words 
20 cubic feet per hour per I.-H.-P. corresponds to say 23 cubic feet 
per Brake H.-P. 

Good coal-gas has a heating power equivalent to about 
500,000 foot-pounds per cubic foot, and hence, with a consump- 
tion of 20 cubic feet the gas-engine succeeds in converting 
nearly 20 per cent, of the energy of the fuel into work. We 
have seen in Chapter Y. that the most efficient steam-engine 
converts only about 15 per cent, of the energy of the fuel into 
-work, and in steam-engines that are small enough to be feirly 
compared with the gas-engines to which these figures refer, the 
fraction converted is rarely more than 10 per cent. The superiority 
of gas-engines over steam-engines, from the thermodynamic point 
of view, is therefore considerable : it is of course due to the greater 
range of temperature through which the working substance is 
carried, and especially to the high mean temperature of the 
working substance during which heat is being taken in, or rather 
being developed by the combustion of the substance itself, a process 
which corresponds to the reception of heat by the working 
substance of an external-combustion engine. 

The following figures are quoted from a Report of trials con- 



ducted by the Society of Arts (1888)*. They relate to three tests 
of a Crossley-Otto engine, of the usual form, which was one of 
three gas-engines submitted for trial. One of the others, the 
Atkinson ''cycle" engine, which was referred to above as having 
a long expansive stroke, had a rather higher efficiency, since it 
consumed only 19*2 cubic feet of gas per l.-H.-p.-hour including 
the supply required for the ignition. The trials quoted below 
were made with the engine working at full power and half power, 
and also running without external load. 

Table XIII. — Trials of a Crossley-Otto Gcts-engine, 

Load Full Power. 

Duration of Trial.... 6 hours. 

Revolutions per minute 
Explosions per minute 
Maximum pressure 
Mean effective pressure 
Indicated H.-P. 
Brake h.-p. 
Mechanical efficiency 
Gas per hour (main) 

„ „ (ignition) 

„ „ (total) 

Gas per i.-h.-p. hour (main) 

„ „ „ (total) 

Gas per B.-H.-P. hour (total) 
Cooling water per hour 
Rise of temperature of cool ) 

ing water J 


197 lbs. 

67-9 „ 


351-8 eft. 

3-5 „ 
355-3 „ 

20-5 „ 

20-8 „ 

24-1 „ 
713 lbs. 


Half Power. 
8 hours. 



196 lbs. 

73-4 „ 




202-6 eft. 

3-2 „ 

205-8 „ 

20-8 „ 

21-2 „ 

27-8 „ 

480 lbs. 

71-3'* F. 

\ hour. 


148 lbs. 

66-7 „ 

490 eft. 

Taking the full power trial, it appears that of every 100 units 
of energy in the fuel, about 22 were turned into work, 43 were 
rejected in the jacket water, and 35 were rejected in the exhaust. 
An indicator diagram of this trial is given in fig. 184, drawn to 
absolute scales of pressure and volume, and with lines BG and EF 
added to illustrate hypothetical compression and expansion 
curves of the form PF'^ss const. An approximation to the real 
compression curve is obtained when n is taken equal 1*38, and 

^ The official report of these trials, with a further desoriptive paper by Professor 
Kennedy (Jour. Soc, Arts.t March 1889), should be referred to as an example of 
a scientific test. 



to the real expansion curve when n is taken equal to 1*435. The 
fact that the last index is higher than the value of 7 for the mixed 
gases shows that heat is being received during expansion (§ 39) 

0-2 0-3 0-4 OS 0-6 0*7 

Volume in cubic feet 
Fio. 184. Otto Engine diagram, Society of Arts' Trials. 

in consequence of after-burning, and notwithstanding the loss to 
the jacket which is going on more actively in this stage of the 
cycle than in any other. The absolute temperature is estimated 
to have been approximately 3440° Fah. at E where it was a 
maximum, 2130° at F after expansion, and 1060° at C after com- 

The loss due to the water-jacket is one of the most serious 
defects of the gas-engine in the present stage of its evolution. 
The water-jacket is necessary only because the combustion 
chamber and the working cylinder are one : by separating them, 
and interposing a cushion of idle air to prevent the hot products 
of combustion from reaching the working surface, it may be hoped 
that this source of loss will eventually be removed. Excessive loss 
also results from the high temperature at which the gases are 
discharged. A partial but important remedy for this is to be 


sought in extending the expansion, as Mr Atkinson has done; 
but the most complete cure is to be looked for in the application 
to gas-engines of the regenerator of Stirling. Though attempts 
in this direction have already been made, the regenerative gas- 
engine still awaits development 

246. Ideal performance of an internal combustion 
engine. That there is an immense margin for improvement in 
the efficiency is clear from the consideration that the gas-engine, 
efficient as it is, falls much more short of the efficiency that 
is theoretically attainable, than does its older rival, the steam- 
engine. In estimating the ideal maximum we may take as the 
lower limit the temperature of the atmosphere, or say 520° Fah. 
(absolute). The trials which have been quoted agree with others 
as showing that an absolute temperature of about 3440° Fah. is 
reached in the combustion of coal-gas under conditions such as 
obtain in gas-engines. If all the heat were generated at this 
temperature the formula 


would be applicable as a measure of the ideal efficiency, to be 
approached, as has just been indicated, by avoiding jacket losses 
and by using a regenerator to assist in making the cycle reversible 
throughout. The value which this fraction takes, with the extremes 
of temperature named above, is 0*85. But in order to bring this 
ideal within reach the gas and air would have to be heated 
separately (by compression and by the use of the regenerator) to 
the maximum temperature before combustion was allowed to 
begin, and would have to be prevented from cooling until com- 
bustion was complete. This would imply an entirely different 
kind of action from that which exists in the Otto or any other 
existing type of engine, where the generation of heat is necessarily 
associated with a rise of temperature. It will be a fairer com- 
parison if we take as the ideal standard of performance that of an 
engine in which the combustion goes on between two defined 
temperatures, a lower initial and a higher final limit, and in which 
the action is reversible in all other respects. Calling Tq the 
temperature to which the gases are raised before ignition, Ti the 
maximum at which (in the ideal case) combustion will be supposed 
to be complete, and t, the lower extremity of the whole range, the 


greatest amount of work that can be done per unit of substance is 

Q>y § 77) expressed by 

w T'^^/ ^ 

Tr= — -(t-Tj) 

•/to T 

T'"! dr (t — Tj) 

J Ti 

if the specific heat during combustion is assumed to be constant 
and equal to a. This makes 

Tr= a (tj - To) - cTTs log. ^' 

and the efficiency 

O- (Ti - To) Ti - To ° To 

Taking the numerical values as above, namely Ti = 3440, 
Ta = 520, and To = 1060, this gives 0*74 as the ideal eflBciency. 

246. Use of cheap gas. At present the gas-engine is chiefly 
known as a motor for small powers, and in such uses the con- 
venience of illuminating coal-gas as fuel compensates for its 
comparatively great cost. But for the application of the gas- 
engine on any large scale a fuel cheaper than illuminating coal- 
gas is essential. In many metallurgical processes a cheap 
gaseous fuel is obtained by letting air pass in a limited quantity 
through incandescent coal or coke ; the gas that passes off 
consists of carbonic oxide formed by union of the carbon with 
the oxygen of the air, diluted by the nitrogen which has 
passed through without change. This "producer gas" as it is 
called is too weak to be effectually used in ordinary gas-engines. 
A stronger fuel called " water gas," consisting of mixed hydrogen 
and carbonic acid, is formed by blowing steam through incan- 
descent carbon. The gas which has hitherto been most used as a 
substitute for common coal-gas in gas-engines has a quality 
intermediate between these two: it is made by Mr Dowson's 
process of sending a jet of mixed air and steam through a chamber 
which contains coke or anthracite at a red heat. The steam 
is formed in a small auxiliary boiler, and blows through a kind of 
injector or jet-pump, in which it takes up air and the two pass 
together into the hot carbon chamber. From it the gas (consisting 
of a mixture of about 25 per cent, of carbonic oxide, with 20 per 
cent, of hydrogen, and the rest nitrogen) is led through " scrubbers" 


into a holder which feeds the engine. The whole plant can 
be erected close to the engine, takes up no great space and requires 
little attention. The gas obtained by this means has only about 
one-fourth of the calorific value of ordinary coal-gas. But by 
restricting the proportion of air admitted to the cylinder and 
compressing the mixture more strongly than is necessarj'^ in the 
case of ordinary coal-gas, the mixture is found to ignite well, 
developing a high initial pressure and giving a diagram resembling 
that given by ordinary coal-gas ^ The mechanical efficiency 
is probably somewhat less than when coal-gas is used, since the 
weaker fuel developes less power per cubic foot swept through by 
the piston. The makers of the " Simplex" engine employ a plant 
for making cheap gas somewhat similar to Mr Dowson's. A 
blowing fan, worked by the engine itself, sends air into the 
bottom of a chamber containing red-hot fuel and at the same time 
a small stream of water is made to trickle upon the grate of the 
chamber, forming steam which rises along with the air; the 
combustible gases produced in this way are led oflF at the top 
through a scrubber to a gas-holder. 

When a gas-engine has its fuel prepared by processes such as 
these a direct comparison becomes possible between its consump- 
tion and that of the steam-engine, since we have to deal in the 
first instance with solid fuel in both cases, supplied at a cost 
per lb. which if not identical is at least readily comparable. 
Messrs Crossley have applied Mr Dowson's process at their own 
works to furnish gaseous fuel for engines developing about 300 
I.-H.-P., and as a result of their experience they guarantee that 
their large engines will not consume more than 1 lb. of anthracite 
or IJ lb. of coke per i.-H.-P.-hour. Trials in other places have 
established that even a small gas-engine may by this means 
develope a horse-power-hour by burning no more than 1 lb, of 
coal. A large steam-engine requires nearly twice as much, 
and a steam-engine small enough to make the comparison 
fair requires three or four times as much fuel. It is therefore not 
surprising that the gas-engine is every day becoming a more 
formidable rival to the steam-engine, for moderately great as well 
as for small powers. Sizes large enough to give some hundreds of 
horse-power are in use, but the mechanical objections to the 

1 For particulars of Mr Dowson's prooess and its application to gas-engines see 
his papers, Min, Proc. Inst, C. E,, Vols, lxxui. lxxxiz. and cxii. 


Otto cycle are more serious in large sizes than in small, and it 
may be conjectured that before large gas-engines become generally 
adopted as substitutes for steamrengines an action will be devised 
which gives a more uniform eflfort and wastes less of the piston's 
movement in idle strokes. 

247. Oil-engines. Liquid fuel may be used in an internal- 
combustion engine either by evaporating it at a low temperature 
and allowing the vapour to pass into the engine mixed with air, to 
be compressed and burnt or exploded there as in gas-engines, 
or by injecting a liquid in the form of a jet or spray into a 
hot chamber where it is converted into a true gas and is then used 
as in a gas-engine. In early petroleum engines the oils burnt were 
of a readily vaporisable class, of low density, and " flashing '* at a 
low temperature. Air was forced through the oil, or the oil was 
stirred up with it or sprayed into it, with the effect that the 
air became charged with combustible vapour. The risk that 
attends the storage and use of such light oils as well as their greater 
cost led to the design of engines in which heavier and less inflam- 
mable oils could be consumed. One of the first of these was the 
Brayton engine (1873), in which air was forced by a compressing 
pump at a pressure of about 60 lbs. per square inch through 
petroleum, after which it passed through a regenerator, heated by 
the exhaust, and was delivered into the cylinder where it was made 
to burn under nearly constant pressure as it entered, expanding in 
volume and causing the piston to perform the working-stroke. This 
method of burning (continuously at nearly constant pressure) is in- 
teresting as a possible alternative to the method usual in gas-engines 
of burning suddenly at nearly constant volume. The Brayton en- 
gine is said to have used 2*7 lbs. of oil per brake horse-power-hour. 
In more modern oil-engines using the Otto cycle the combustion 
has been reduced to about one-third of this amount. In their 
main mechanical features and in the use of a water-jacket to cool 
the cylinders these engines do not differ from gas-engines. 

The Piiestman engine has a separate vaporising chamber, into 
which oil is sprayed along with air from a closed tank. The tank 
is partly full of oil, and the air above it is kept at a moderate 
pressure by means of a small pump. Two pipes leading from the 
air and oil spaces respectively are united to form a spraying 
nozzle which delivers a stream of finely divided oil mixed with 
a little air into the vaporising chamber. This chamber is heated 


by the exhaust gases to a temperature of 200'' to 300"* F. Before 
the engine starts the vaporiser is heated by a special oil flame. 
The vaporised oil is drawn into the cylinder in the suction stroke, 
along with a large additional quantity of air, then compressed by 
the working piston, exploded and exhausted as in other engines of 
the Otto type. A little of the vapour is condensed during 
compression, and this serves to lubricate the cylinder. Ignition 
is by an electric spark, and the governor acts by adjusting the 
amount of oil and air admitted to the vaporiser through the 
spraying nozzle. The proportion of oil to air is maintained, 
so that the engine has an explosion at every second revolution 
whether the load is heavy or light, but the energy of the explosion 
is varied to suit the load\ 

In the Homsby-Ackroyd engine, which is remarkable for 
its simplicity, the oil is rendered gaseous in a small hot chamber 
which forms an extension of the cylinder and in which the 
explosion subsequently occurs. The explosions keep the chamber 
at a high temperature ; before the engine starts it is heated by 
an outside oil-lamp furnished with a blowing fan. The oil required 
for each explosion is pumped into this chamber, which, when 
the oil enters is full of the hot products of combustion from the 
previous stroke. The oil is converted into gas which does not at 
first ignite, no fresh air being present and the temperature being 
barely high enough in any case. Meanwhile the piston has 
drawn in air during the forward stroke, and when this is com- 
pressed during the next back stroke some of it enters the hot 
chamber ; at the same time the temperature of the air is raised 
by compression, and the result is that the explosion takes place 
just as the piston passes its dead point. It is found that no 
special appliance such as a timing value or an electric spark 
is necessary to secure that ignition shall occur at the proper 
place of the stroke. What is required is that the amount of 
compression shall be suitable. Too much compression would 
make the mixture ignite prematurely, before the piston reaches 
the end of its back-stroke ; and provision is made to adjust the 
amount of compression, so that ignition may be neither early nor 
late, by shortening or lengthening the connecting rod, which has 
the eflfect of enlarging or reducing the clearance. The governor 
acts by throttling the suction of the oil-pump with the effect 

1 Min. Proc» Inst. C, £., Vol. cix., 1892. 



that the explosive mixture is weakened when the speed rises. 
An indicator diagram from one of these engines is given in 
fig. 185, with a scale of pressures marked at the side. Messrs 
Crossley make a similar engine, in which the vaporising or 









Fio. 185. Indicator diagram of Homsby-Aokroyd Oil-engine. 

gasif3dng chamber is kept hot by an external flame throughout 
the action, and the compressed mixture is ignited by a hot tube 
and timing value as in their gas-engine. The governor prevents 
any explosive mixture from entering the cylinder when the 
speed exceeds its normal amount. A great variety of other 
oil-engines, with actions more or less similar to those that have 
been named, are sold by firitish and Continental makers. 

Professor Un win's tests of a Priestman engine indicating eight 
or nine horse-power at full load showed a consumption of 0*84 lbs. 
per l.-H.-P.-hour when the petroleum was of a quality known 
as "Daylight" oil, and 0*95 to 0*99 lbs. when a rather heavier oil 
called Russolene was used. The calorific value of the oils, 
allowing for the fact that part of the burnt products escaped in 
the form of steam, was about 19500 thermal units in both cases, 
but it appeared that the lighter oil vaporised more easily and 
completed its combustion earlier in the stroke. The following 
table is given for a full-power trial with Russolene as fuel. 

Table XIV. Performance of Priestman's Oil-engine, 
Heat due to combuHtion of oil 100 per cent. 
Work done on Brake 
Engine friction 
Indicated work 
Heat rejected to jacket water 
„ ,, in exhaust gases 

13-3 , 

2-8 , 

16.1 , 

47-5 , 

26-7 , 




The remainder, amounting to between 9 and 10 per cent., was 
lost by radiation or otherwise unaccounted for. The thermo- 
djmamic efficiency (016) is not much less than that of a gas- 
engine, and very much greater than that of a steam-engine of the 
same size. 

The oil-engine shares with the gas-engine, though in rather 
less degree, the advantage of requiring but little attention ; it 
can be used in situations where there is no supply of gas, and 
the cost of oil per horse-power-hour is less than that of town 
gas. For engines of large power a cheaper fuel is obtained by 
producing gas from coke or from cpal, but as a small power 
motor at once convenient and inexpensive the oil-engine cannot 
fail to take an important place^ 





Pressnie in 

Volume of lib. 
in cubic feet 

lbs. per Bq. in. 







































































163 A 
























































































PrensTue in 

Volnme of lib. 
in cubic feet 

lbs. per gq. in. 





















































































































































































































Pressure in 

Volume of lib. 
in cubic feet 

lbs. per sq. in. 







































. 0-506 














821 ; 











































381- ; 


























391 ;; 







. 0-557 






















The temperatnres are stated to the nearest half degree Fahrenheit. 

The yolumes are calculated from Begnault's data, taking 778 foot-pounds as the 
value of J, • 

^w is the entropy of water, per lb., at the temperature at which steam would 
be formed under the assigned pressure, the entropy of water at 32° Fah. being used 
as the zero from which <f> is reckoned. 

0« is the entropy of saturated steam, per lb., reckoned from the same zero. The 

quantities </>, and ^^ are connected by the equation <f>,-<p„=—, 


For values of H and h see Table I. p. 65. 


Absolate temperature, 40 

Lord Kelvin's scale, 86 

Absorption dynamometer, 192 
Adiabatio expansion, 46 

of steam, 72 

formula for, 

74, 97 

Admission, 81 

Aeolipile, 2 

After-burning in gas-engines, 374, 376 

Air, compressed, transmission of power 

by, 127 
Air cushion in single-acting engines, 

294, 332 
Air-engines, 357 

with regenerator, 60, 358 

Stirling's, 60, 358, 361 

Ericsson's, 61, 361 

—0- Joule's, 117 

using Camot's cycle, 358 

Bobinson's, 362 

Bider's, 363 

using internal combustion, 365 

Buckett's, 365 

Cayley's, 365 

Wenham's, 365 

Air-pump first applied to steam-engines 

by Watt, 12 
Air, supply of, to furnace, 299 
Air thermometer, 87 
Air, values of constants for, 44 
Allan's link-motion, 234 
Allen's governor, 277 
American river steamers, 28 

Ammonia, use of in refrigerating ma- 
chines, 119 

Angular advance, 216 

Antipriming pipe, 307 

Appendix : Table of properties of steam, 

Armington and Sim's governor, 269 

Atkinson's gas-engines, 371, 372 

Atlantic liners, modern, 29 

Atmospheric gas-engine of Otto and 
Langen, 368 

Une, 172 

steam-engine of Newco- 

men, 9 

Babcock and Wilcox boiler, 310 

Back pressure, 81, 133 

Balance piston, 247 

Balancing of mechanism, 294 

Barrel calorimeter, 183 

Barrus calorimeter, 184 

Beam engines, 325 

Beau de Bochas, 368 

Beighton, Henry, 11 

Bell, Henry, 28 

Bell-Coleman refrigerating machine, 121 

Belleville boiler, 310 

Bell's "Comet," 346 

Bilge pump, 349 

Binary vapour engine, 127 

Bischoff's gas-engine, 367 

Bishop's disc engine, 341 

Bissel pony truck, 352 

Black's doctrine of latent heat, 17, 30 



Bleohynden on the development of the 

marine engine, 29 
Bogie, 861 

Boiler and Fumaoe efficiency, 167 
Boiler mountings, 807 
Boilers, 298 

Oomish, 28, 808 

Lancashire, 808 

Multitubular, 307 

Vertical, 808 

Watertube, 809 

Locomotive, 812 

Marine, 816 

use of zinc in, 820 

Boulton, M., 21 

Bourdon pressure gauge, 807 

Boyle's Law, 89 

Brake dynamometer, 192 
Brake horse-power, 167, 192 
Bramwell, Sir F. , on marine engines, 29 
Branca*s steam turbine, 4 
Brayton's petroleum engine, 888 
Bremme's valve gear, 238 
Brotherhood's three^ylinder engine, 830 
Bull engiiie, 28, 826 

Cameron and Floyd's steam-pump, 386 
Gamot, Sadi, his contributions to the 
theory of heat-engines, 30 

conception of a cycle of opera- 
tions, 38 

Gamot's cycle with a gas for working 
substance, 60 

efficiency in, 62 

with steam for Working 

substance, 76 

Gamot's principle, 64 

applied to determine 

the influence of pressure on the tem- 
perature at which change of physical 
state occurs, 87, 90 

Gataract of Gomish engines, 26, 260 

Gawley, 9 

Centrifugal governors, 268 

** Century of Inventions," the, 4 

Charles's law, 89 

** Charlotte Dundas," the, 28 

Cheap gas for use in gas-engines, 881 

Chimney draught, 299, 302 

Circulating pump, 349 

Clark, D. E., on initial condensation of 
steam in the cylinder, 186 

Glausius, his contributions to the theory 
of heat-engines, 30, 98 

his statement of the second 

law, 86 

Clearance, 184 

Clerk's gas-engine, 871 

Clerk's experiments on the explosive 
combustion of gases, 376 

Closed stokehole, 321 

Coal, calorific value of, 168 

consumption of in marine engines, 


Coal gas, thermal value of, 377 

Coefficient of Performance in refrigera- 
ting machines, 120 

" Comet," the. 28 

Compound expansion, 23, 196 

advantages o^ 24, 

164, 206 

Compound refrigerating machine, 124 
Compound indicator diagrams, 198, 202, 

Compound locomotive, 362 
Compressed air, transmission of power 

by, 127 
Compression of steam into the clearance 

space, 134 
Compression essential to efficiency in 

certain air and gas engines, 366, 368 
Condensation and reevaporation of steam 

in the cylinder, 136; exhibited in the 

entropy temperature diagram, 142 
Condenser, invention of by Watt, 11 
Condensing engines, ideal performance, 

results of trials, 

161, 166 

Condensing water, measurement of^ 186 
Conical pendulum governors, height of, 

Connecting-rod, inertia of, 286 
Conservation of energy, 38 
Controlling force in governors, 266, 268 ; 

curves of, 266 
Corliss engines, trials of, 148, 161 

indicator diagrams from, 

gear, 270, 828 


Cornish Boiler, 23, 303 

Cornish pumping engine, 25, 250, 334 

Corrugated flues, 316 

Cotterill, Prof., 114 

Coupled engines, 327 

Cowper, E. A., 27 

Crampton's dust fuel furnace, 322 

Crank shaft, work on the, 280 

Crank effort, diagram of, 280, 288 

Crosby Indicator, 170 

Crossley-Otto gas-engine, 369 

trials of, 378 

Cugnot's road locomotive, 23 
Curve of expansion to be assumed in 
estimates of probable horse-power, 168 
Cut-off, 81 
Cushion-steam, 136 
Cushioning, 135, 218 
Cycle of operations in a heat-engine, 37 

in Camot's engine, 


in steam-engines, 81 

Cylinder feed, 136 

walls, influence of, 136 

volumes, ratio of in compound 

engines, 204 

Donkin, Bryan, experiments, 140, 146, 

Double ported slide>valve, 246 
Double-beat valve, 250 
Dowson's process for making cheap 

gaseous fuel, 366, 381 
Draught, natural and forced, 299, 302 
Drop in the receiver, 198 

adjustment of, 201 

Dryness of wet steam, 70 

change of in adiabatic 

expansion, 72, 109, 

affected by throttling 

or wire drawing, 91, 

measurement of, 183, 


Du Tremblay's binary engine, 127 
Dudgeon^s rotary engine, 340 
Dunlop's pneumatic governor, 279 
Durham and Churchill's governor, 277 
Dust fuel, 322 

* Duty* of an ^igine, 25, 157 
Dwelshauvers-Dery, 190 
Dynamometer, rope, .192 

Dalby,W. E., 231, 245 

Dash-pot, 269 

Davey, H. , differential valve gear, 278 

pumping engine, 334 

safety motor, 339 

De Caus, 3 

Delia Porta, 3 

Degradation of temperature in a heat- 
engine, 36 
Density of saturated steam, 64, 87 
Desaguliers, 7 
Diagonal engines, 347 
Diagram factor, 168 

of crank-effort, 280, 288 

circular, 290 

Differential gear for relay governor, 275 
Differential or dynamometric governors, 

Differential valve gear, 278 
Differential gas-engine (Atkinson's), 371 
Disengagement governors, 274 
Direct-acting engines, 324, 326 
Distribution of steam, 221 

Eccentric used to actuate slide-valve, 215 
Effective horse-power, 167 
Efficiency of a heat-engine, 1, 35 

of a perfect engine, 56 

of ideal steam-engines, 78, 


of boiler and furnace, 157 

mechanical, 167 

maximum, conditions of, 57 

of gas-engines, 377 

Ejector condenser, 320 
Elder, John, 27 

Emery, 137, 159 

Engine receiving heat at various tem- 
peratures, 92 
Engine trials, summary of results, 159, 
161, 166 

example of, 187 

English, Col., 137 
Entropy, 98 

of steam, 100, 107, 109 

temperature diagrams, 100, 103, 

106, 108, 112, 114, 117 



Entropy temperature diagrams, for 
steam, 102, 108 

temperature diagram, for saper- 

heated steam, 102 

temperature diagram, use of in 

exhibiting the exchanges of heat be- 
tween the working substance and the 
cylinder, 142 

Entropy of water and steam, 109, 387 
Equilibrium of governors, condition of, 
265, 256, 257 
valve in Watt's engine, 13, 

Equivalent eccentric in link-motions, 

Ericsson's regenerative air-engine, 61, 

Ether, use of in refrigerating machines, 
along with steam in heat-engines, 

Evans, Oliver, 23 
Exchange of heat between the steam and 

the cylinder walls, 81, 190 
Exhaust, 81 

Exhaust steam injector, 319 
Expansion, complete and incomplete, 83 
Expansion-valve, 240 

Meyer's, 241 

Expansive use of steam by Watt, 20 
Experiments on steam-engines, results 

of, 148, 150, 151, 153, 159, 161, 166 

Feed-water, measurement of, 179 

comparison of, with dis- 

charged water, 182 

heater, 299, 320 

Field tubes, 309, 310 

Fielding's engine, 341 

Fireless tramway locomotive, 354 

Flames, applied to heat the cylinder in 

Donkin's experiments, 146 
Fletcher, L. E., 306 
Fly-wheel, function of, 280, 290 
Forced draught, 321 
Forms of the steam-engine, 324 
Four-stroke cycle of Beau de Boohas and 

Otto, 868 
Fox, S., 317 
Franoq, L6on, 354 

Friction of slide-valves, 247 

governors, 264 

engine, 282, 217 

Fulton, B., 28 

Furnace and boiler efficiency, 157 
Furnace, supply of air to, 299 
Fusible plug, 307 

Galloway tubes, 303, 309 

boiler, 306 

Gases, permanent, laws of, 39 

Gkfcs and air, explosion of mixtures of, 375 
Gas-engine cycle of Beau de Boohas, 368 
Gas-engines, 355 

early forms, 367 

Lenoir's, 367 

Hugon's, 367 

Bischoff's, 367 

Otto and Langen's, 367 

Otto's, 369 

Simplex, 370 

Atkinson's, 371 

Clerk's, 371 

Griffin, 372 

performance of, 377, 382 

Gauging the discharge from the con- 
denser, 186 

Gibbs, J. Willard, 101 
Giffard's injector, 318 
Gooch's link-motion, 234 
Governing, 252 
Governors, centrifugal, 253 

Watt's, 21, 263 

loaded, 253, 262 

spring, 254, 263, 269 

height of, 256 

BtabiUty of, 256, 259 

sensibility of, 259 

parabolic, 260 

power of, 264 

disengagement, 274 

supplementary, 274 

relay, 275 

differential or dynamometric, 


pump, 278 

for marine engines, 279 

Graphic representation of work done in 

the changes of volume of a 
fluid, 36 



Graphic representation of resolts of trial 
made under yarious amounts 
of load, 194 

method of examining the action 

of a slide-valve, 219 

solution of the link-motion, 235 

Ghray, J. MaoFarlane, 101, 236 
Griffiths, experiments on the mechanical 

equivalent of heat, 35 
Gunpowder engines, 7 

Hackworth's radial valve-gear, 237 
Hall, surface condenser, 348 
Hall's pulsometer, 338 
Hallauer, 137, 148 
Harmonic valve diagram, 229 

applied to 

Meyer's expansion valve, 244 

Harrison's boiler, 310 
Hartnell, spring governor, 254 
Head, J., parabolic governor, 260 
Heat, mechanical equivalent of, 33, 34 

weight, 93 

Pumps, 118 

supplied, measurement of, 183 

rejected, measurement of, 185 

Heat-engine, defined, 1 

limiting efficiency of, 56 

reversible, 54 

Heating surface, 298 
Hero of Alexandria, 2 
Herreshof boiler, 310 
Hill, J. W., 139, 161 ^ 
Him, 71, 137, 190 

History of the steam-engine, 1 
Holden, H., use of liquid fuel, 323 
Hooke's joint as a basis of rotary engines, 

Horizontal direct-acting engines, 327 
Hornblower's early compound engine, 23 
Horse-power, 7 ; its value fixed by Watt, 

estimation of, 168 

measurement of by the in- 

dicator, 176 

brake, measurement of, 


Howden, 321 

Hugon's gas-engine, 367 

Hunting, 268 

Huygens, 7 
Hydrokineter, 319 

Hyperbolic logarithms, relation of to 
common logarithms, 49 

loe-making machines, 121 
Ignition tube in gas-engines, 370 
Imperfectly resisted expansion, 58, 91 
Inclined cylinder engines, 324 
Incomplete expansion, 83, 112, 131 
Indicated horse-power, calculation of, 176 
Indicator, the, 21, 167, 172 

diagram, 37 

directions for taking, 


typical form in a con- 

densing steam-en- 
gine, 132 

examples of in steam- 

engines, 177, 208, 

combination of in 

compound engines, 

of Lenoir gas-engine, 


of Otto gas-engine, 

374, 375, 379 

of the Homsby Ack- 

royd oil-engine, 385 

Inequality of distribution of steam by 

the slide-valve, 222 
Inertia of reciprocating pieces, 283, 335 
Initial condensation, 137« 144 
Injector, 318 
Inside lap, 217 
In-stroke, 220 

Internal combustion-engine, 117, 357; 
ideal performance of, 380 

energy of a gas, 42 

of steam, 69 

Isherwood, 186 

Isochronism in governors, 259, 261 
Isothermal expansion, 48 

lines for steam, 71 

Jacket, steam, invented by Watt, 12 
Jacket-steam, measurement of, 182 
Jenkin, Fleeming, regenerative gas- 
engine, 61 



Joule's experiments on the meohanioal 
equivalent of heat, 80, 84 

law of the internal energy of 

gases, 42, 87 

air-engine, 116 

reversed, 121 

Joy's radial valve-gear, 288 
Jukes's furnace, 322 

Kelvin, Lord, his contribution to the 
theory of heat-engines, 80 

his statement of the second law, 


his scale of absolute tempera- 

ture, 86 

experiments with Joule on the 

specific heats of gases, 87 

on warming by reversal of the 

heat-engine cycle, 124 
Kennedy, Prof., trials of steam-engines, 
180, 164 
— — trials of boilers, 812 

trials of gas-engines, 878 

Kirk, A. C, 119, 239 
Knocking at joints, 298 
Knowles*B governor, 274 

Lagging of steam-pipes, 138 
Lap in valves, 216 

negative, 247 

Latent heat, Black's doctrine of, 17, 80 

of steam, 67 

Laval, de, steam-turbine, 846 
Lead in valves, 186, 216 
Leavitt, 168, 167 

Lenoir's gas-engine, 367 

Leupold, 22 

Lightfoot's refrigerating machine, 124 

Limits of temperature determining the 

efficiency in perfect heat-engines, 56 
Link-motion, 238 
Liquid fuel, 322 
Loaded governor, 268, 257 
Locomotive, earliest use of steam in, 28 

use of on railways, 28 

balancing of, 296 

boilers, 812 

forms of, 850 

compound, 852 

Loring, 187 

Loss of heat in engines, 155 

in boiler and furnace, 801 

Mair-Bmnley, 161, 187 

Mallet, A., compounding of locomotives, 

Marine boilers, 815 

engines, 346 

Marshall's valve-gear, 288 

Marshall, F. C, on marine engines, 29 

Marshall and Weighton, 849 

McNaught, 26, 169 

Mean effective pressure, 176 

Mechanical equivalent of heat, 38, 84 

production of cold, 118 

efficiency, 167, 193 

tests of, 192 

advantage of compound ex- 

pansion, 206 

stoking, 822 

Mekarski tramway locomotive, 855 
"Miner's friend," the, 6 
Morton's Ejector Condenser, 320 
Murdoch, 21, 340 

Mushroom valve, 250 

Napier's governor, 277 

Newcomen's atmospheric steam-engine, 

Niclausse Boiler, 310 
Non-condensing engine, 21 

results of trials, 

Non-lifting injectors, 319 
Non-rotative engines, 824 
Notching-up, 284 

Oil as furnace fuel, 828 
Oil-engines, 888 

Brayton, 883 

Priestman, 883, 885 

Hornsby Ackroyd, 884 

performance of, 885 

indicator diagram of, 885 

Organs of a steam-engine, 79 
Oscillating cylinder engines, 825, 847 
Otto and Langen's gas-engine, 867 
Otto's gas-engine, 869 

action in the cylinder 

of, 878 



otto's gas-engine, indicator diagrams of» 

374, 375, 379 
Outside lap, 217 
Out-stroke, 220 
Oval valve diagram, 228 

Papin, Denis, 7, 8 
Parallel motion, 325 
Parson's steam-turbine, 342 
Peabody*s calorimeter, 184 
Peauoellier linkage, 326 
Perfect gas, 38 

heat-engine, 56 

Performance of engines, methods of 

stating, 156 
Perkins, Loftus, 310 
Piston speed, 29, 350 

valves, 49 

and piston-rod, inertia of, 284 

Petroleum as fuel, 322 

engines, 383 

Pole, W., 27 
Porter's governor, 253 
Potter, Humphry, 10 
Power of governors, 264 

of marine engines in relation to 

their weight, 349 

Pressure, volume, and temperature, re- 
lation of in gases, 41 

and temperature of saturated 

steam, 35, 387 

and volume of saturated steam, 

64, 387 

Pre-admission, 136, 218 
Pre-heater, 130 
Priestman's oil-engine, 383 
Priming, 157 
Producer gas, 381 
ProU's governor, 262 

trip-gear, 273 

Properties of steam, 62, 387 
Pulsometer, 338 
Pumping engines, 334 

Badial valve gear, 233, 237 

axle box, 352 

Bamsbottom safety-valves, 314 
Bankine's contribution to the theory of 

heat-engines, 30 

statement of the second law, 85 

Eansome, H. B., experiments on fluctua- 
tion of speed, 292 
Batio of expansion, 45 

influence of on the 

efficiency, 146, 148 

Batio of cylinder volumes in compound 

engines, 204 
Beceiver in compound engines, 197 

engine, 198 

drop in the, 198 

Beciprocating pieces, effect of their 

inertia, 283 
Befrigerating machines, 118 

coefficient of perfor- 

mance in, 121 

the Bell-Coleman, 


Begenerator, Stirling's, 59 

entropy temperature dia- 

grams in engine using a, 

use of, in air-engines, 60, 

358, 361, 363 

use of, in refrigerating 

machines, 119 

application of, to steam and 

gas engines, 61 
Begnault's experiments on the properties 

of steam and gases, 30, 41, 63, 67 
Belease, 81 

Beuleaux, slide-valve diagram, 222 
Belief frames, 247 
Besults of trials, summary of, 166 
Betum connecting-rod engine, 347 
Beversal of cycle in heat-engines, 54, 

of thrust at joints, 292 

Beversibility in heat-engines, 54, 55 

in refrigerating machines, 


conditions of, 58 

approach to in steam- 
engines, 81 

Beversing gear, 232 

Beynolds, Prof. O., trials of engines, 

Harmonic valve 

diagram, 231 

Bichard's indicator, 169 
Bitter, 71 



Boad looomotives, 855 

Bobinson's Bystem of mechanical philo- 
sophy, 15 

Booking slide-valve, 249 

Boot's boiler, 310 

Bope brake, 192 

Botary engines, 325, 339 

Bowland on the mechanical equivalent 
of heat, 34, 87 

Bussian locomotives, use of liquid fuel 
on, 323 

BuBsolene oil, 385 

Safety Motor (Davey), 339 
Safety-valves, 307, 314 
Saturated steam, 63 

properties of, 66 

Saturation curve on the indicator dia- 
gram, 140, 211 

Savory's engine, 6, 338 

Schroter, Prof., trials of engines, 166 

Self-starting injectors, 319 

Side-lever engine, 346 

Siemens, Sir W., 61, 276 

" Simplex" gas-engine, 370, 382 

Single acting engines, 292, 329 

Size of an engine, influence of on the 

efficiency, 146 
Slide-valve, 215 

forms of, 246 

diagrams, 217, 219, 220, 222, 

223, 224 

Smeaton, 11 
Smith, Prof. B.H., 201 
Society of Arts trials of gas-engines, 378 
Somerset, Marquis of Worcester, 4 
Specific heats of gases, 41, 43 
Speed, mfluence of on the efficiency, 
146, 150 

peri^p^io fluctuation of, 290 

Spenoer-Inglis trip gear, 272 
Spherical engine, 341 

Spring governors, 264, 263 
Stability in governors, 266 
Steam, formation of under constant 
pressure, 62 

saturated and superheated, 63 

determination of the properties 

of by Begnault, 63 

entropy of, 109 

Steam, table of properties of, 65, 387 

production of, 298 

Steam-engine, early history of, 1 

working without compres- 
sion but with complete adiabatic ex- 
pansion, 93, 102 

Steam-gas, 70 
Steam-jacket, 12 

action of, 144, 151 

Steam-ships, introduction of, 28 
Steam-turbines, 325, 342 
Steeple-engine, 346 
Stephenson, George, 23 
Stephenson's link-motion, 233 
Stirling, B., his invention of the Be- 

generator, 59 
Stirling's regenerative air-engine, 60, 

theoretical indica- 

tor diagram of, 60 


diagram of, 114 

performance of, 360 

modern forms of, 361 

Stoking, mechanical, 322 
Superheated steam, 63, 70, 106, 152 

influence of in re- 

ducing the initial 
condensation, 152 

used in steam tur- 
bine, 345 

Superheater, tubular, 320 

Sulzer engine, trials of, 153, 165, 261 

Supply of steam, measurement of by 

means of the feed, 


measurement of by 

means of the condensed water, 181 

Surface condenser, used by Watt, 12 

— - in marine use, 348 

Swing-bolster, 352 

Tail-rod, 327 

Tandem-engines, 197, 328 

Tangye, spring-governor, 254 

Tanks, arrangement of for measuring 

the feed, 181 
Temperature, absolute, 40 

relation of to pressure and 

volume in gases, 41 



Temperature, change of in the adiabatio 
expansion of a gas, 47 

of source and receiver of 

heat in a perfect heat-engine, depen- 
dence of efficiency on, 56 

Temperature reached in the explosion 
of gaseous mixture, 376 

Theory of heat-engines, development of, 

Thermodynamic function, 98 

Thermodynamics, laws of, 33, 35 

Thompson, W. B., device for governing 
marine engines, 279 

Thomson, B. W. , road steamer, 355 

Thomson, W. (see Kelvin). 

Thomycroft water-tube boiler, 311 
high speed engines, 329 

Throttle-valve, 21, 270 

Throttling of steam, 91 

Throttling calorimeter, 184 

Timing valve in gas-engines, 370 

Total heat of steam, 68 

Tower's spherical engine, 341 

Traction-engines, 355 

Tramway locomotives, 354 

Transmission of power by compressed 
air, 127 

Travel of valve, 218 

Trevithick, 23 

Trials of steam-engines, summary of 
results of, 159, 161, 166 

example of, 187 

under various 

amounts of 
load, 193 

methods of con- 
ducting, 179, 181, 185, 192 

of steam-turbine, 344 

of gas-engine, 378 

of oil-engine, 386 

Trick valve, 246 
Trip-gear, 270, 272, 273 
Triple expansion, 29 

advantage of in utiliz- 
ing high- pressure steam, 206 

Triple expansion engines, trials of, 166, 
209, 212 

weight of, 360 

diagrams, combination 

of; 213 

Trunk-engines, 325 
Turbine, Parson's steam, 342 

De Laval's steam, 346 

Unwin, Prof., trials of steam-engines, 
151, 154, 162 

trial of oil-engine, 385 

Urquhart, T., use of liquid fuel, 323 

Vacuum in condensers, 133 
Valve diagram, Beuleaux's, 222 

Zeuner's, 225 

Oval, 228 

Harmonic, 229 

Valves and valve-gears, 215 

double beat, 250 

double-ported, 246 

expansion, 240 

Meyer's, 241 

of Cornish engines, 250 

piston, 249 

slide, 214 

forms of, 246, 249 

timing, in gas-engines, 370 

Trick, 247 

Vertical engines, 329 

Volume, relation of to temperature and 
pressure in gases, 41 

of saturated steam, 64, 87, 387 

Volume-pressure diagrams, 37 

Walshaert's valve-gear, 239 

Water-gas, 381 

Water-jacket used in gas-engines, 367 

Water-tube boilers, 309 

Watt, James, 11 

experimental apparatus, 11, 15 

invention of the condenser, 11 

first patent for improvements in 

the steam-engine, 12 

narrative of his invention, 16 

governor, 21, 263 

sun and planet wheels, 19 

double-acting engine, 19 

expansive use of steam, 20 

invention of the indicator, 21 

parallel motion, 20, 326 

Webb, F. W., 352, 353 
Weight of marine engines in relation to 
their power, 349 



Weir for gauging oondenBing water, 

Weir's hydrokineter, 319 
Westinghoofle engine, 832 
Wet steam, 70 
Wetness of steam in the cylinder, 189 

how measured, 189 

Wheel-engines, 340 

Willans' trials of engines, 149, 160, 198 

line, 195, 346 

central valve engine, 380, 882 

Winding engines, 827 

Wingfield, C. H., 168 
Wire-drawing of steam, 91, 182 
Woolf , 24 

engines, 197, 828 

Worcester, Marquis of, 4 

Work measured by the area of the indi- 
cator diagram, 37 

theoretically attainable from lib. 

of steam, 163 
Working substance in a heat-engine, 1, 

WorsdeU, T. W., 358 
Worthington high-duty pumping engine, 
337 ; trials of, 162, 167 
steam-pump, 336 

Yarrow water-tube boiler, 812 

Zeuner, 64, 71, 93 

his valve diagram, 225 

applied to 

Meyer expansion valves, 242 

Work done by an expanding fluid, 36, Zinc, used to prevent corrosion in 
44 boilers, 320 




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U De'4g 

J No. 291^ 


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